691 results on '"Colliot P"'
Search Results
102. Generating PET-derived maps of myelin content from clinical MRI using curricular discriminator training in generative adversarial networks
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Colliot, Olivier, Mitra, Jhimli, Soulier, Théodore, Hamzaoui, Mariem, Sales Pitombeira, Milena, De Paula Faria, Daniele, Yazdan-Panah, Arya, Tonietto, Matteo, Leroy, Claire, Bottlaender, Michel, Bodini, Benedetta, Burgos, Ninon, Ayache, Nicholas, Colliot, Olivier, and Stankoff, Bruno
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- 2024
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103. AD Course Map charts Alzheimer’s disease progression
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Koval, Igor, Bône, Alexandre, Louis, Maxime, Lartigue, Thomas, Bottani, Simona, Marcoux, Arnaud, Samper-González, Jorge, Burgos, Ninon, Charlier, Benjamin, Bertrand, Anne, Epelbaum, Stéphane, Colliot, Olivier, Allassonnière, Stéphanie, and Durrleman, Stanley
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- 2021
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104. Universal unramified cohomology of cubic fourfolds containing a plane
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Auel, Asher, Colliot-Thélène, Jean-Louis, and Parimala, R.
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Mathematics - Algebraic Geometry ,11E20, 11E88, 14C25, 14D06, 14E08, 14E08, 14F22, 14J28 - Abstract
We prove the universal triviality of the third unramified cohomology group of a very general complex cubic fourfold containing a plane. The proof uses results on the unramified cohomology of quadrics due to Kahn, Rost, and Sujatha., Comment: 20 pages, comments welcome
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- 2013
105. Rationalit\'e d'un fibr\'e en coniques
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Colliot-Thélène, Jean-Louis
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Mathematics - Algebraic Geometry ,14M20, 14E08, 14F22, 12G05 - Abstract
F. Campana had asked whether a certain threefold is rational. In arXiv:1310.3569v1 [mathAG], this variety was shown to be birational to a specific conic bundle and then to be unirational. We prove that this conic bundle is rational., Comment: in French
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- 2013
106. Pathologies of the Brauer-Manin obstruction
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Colliot-Thélène, Jean-Louis, Pál, Ambrus, and Skorobogatov, Alexei N.
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,14G05, 14F22 - Abstract
We construct a conic bundle over an elliptic curve over a real quadratic field that is a counterexample to the Hasse principle not explained by the \'etale Brauer-Manin obstruction. We also give simple examples of threefolds with the same property that are families of 2-dimensional quadrics, and discuss some other examples and general properties of the Brauer-Manin obstruction., Comment: 22 pages, to appear in Mathematische Zeitschrift
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- 2013
107. Descente galoisienne sur le second groupe de Chow : mise au point et applications
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Colliot-Thélène, Jean-Louis
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Mathematics - Algebraic Geometry ,Mathematics - K-Theory and Homology ,19E15, 14F42, 14C25, 14F20 - Abstract
Connections between the second Chow group of a smooth projective variety and its third unramified cohomology group, with coefficients the roots of unity twisted twice, feature in several recent works. In this note we revisit a 1996 paper by B. Kahn and specialize it to various types of rationally connected varieties., Comment: In French. Final version, to appear in Documenta math. Section 5 contains a discussion of the universal unramified third cohomology group for Fano hypersurfaces, and in particular for cubic hypersurfaces
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- 2013
108. Lois de r\'eciprocit\'e sup\'erieures et points rationnels
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Colliot-Thélène, Jean-Louis, Parimala, Raman, and Suresh, Venapally
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,11G99, 14G99, 11E72, 14F22 - Abstract
Let C be the complex field and K=C((x,y)) or K=C((x))(y). Let G be a connected linear algebraic group over K. Under the assumption that the K-variety G is K-rational, i.e. that the function field is purely transcendant, it was proved that a principal homogeneous space of G has a rational point over K as soon as it has one over each completion of K with respect to a discrete valuation. In this paper we show that one cannot in general do without the K-rationality assumption. To produce our examples, we introduce a new type of obstruction. It is based on higher reciprocity laws on a 2-dimensional scheme. We also produce a family of principal homogeneous spaces for which the refined obstruction controls exactly the existence of rational points., Comment: Final version, in French, to appear in the Transactions of the American Mathematical Society
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- 2013
109. Cohomologie non ramifiée dans le produit avec une courbe elliptique
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Colliot-Thélène, J.-L.
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- 2019
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110. Clinica: An Open-Source Software Platform for Reproducible Clinical Neuroscience Studies
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Alexandre Routier, Ninon Burgos, Mauricio Díaz, Michael Bacci, Simona Bottani, Omar El-Rifai, Sabrina Fontanella, Pietro Gori, Jérémy Guillon, Alexis Guyot, Ravi Hassanaly, Thomas Jacquemont, Pascal Lu, Arnaud Marcoux, Tristan Moreau, Jorge Samper-González, Marc Teichmann, Elina Thibeau-Sutre, Ghislain Vaillant, Junhao Wen, Adam Wild, Marie-Odile Habert, Stanley Durrleman, and Olivier Colliot
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neuroimaging ,software ,pipeline ,data processing and analysis ,machine learning ,multimodal neuroimaging data ,Neurosciences. Biological psychiatry. Neuropsychiatry ,RC321-571 - Abstract
We present Clinica (www.clinica.run), an open-source software platform designed to make clinical neuroscience studies easier and more reproducible. Clinica aims for researchers to (i) spend less time on data management and processing, (ii) perform reproducible evaluations of their methods, and (iii) easily share data and results within their institution and with external collaborators. The core of Clinica is a set of automatic pipelines for processing and analysis of multimodal neuroimaging data (currently, T1-weighted MRI, diffusion MRI, and PET data), as well as tools for statistics, machine learning, and deep learning. It relies on the brain imaging data structure (BIDS) for the organization of raw neuroimaging datasets and on established tools written by the community to build its pipelines. It also provides converters of public neuroimaging datasets to BIDS (currently ADNI, AIBL, OASIS, and NIFD). Processed data include image-valued scalar fields (e.g., tissue probability maps), meshes, surface-based scalar fields (e.g., cortical thickness maps), or scalar outputs (e.g., regional averages). These data follow the ClinicA Processed Structure (CAPS) format which shares the same philosophy as BIDS. Consistent organization of raw and processed neuroimaging files facilitates the execution of single pipelines and of sequences of pipelines, as well as the integration of processed data into statistics or machine learning frameworks. The target audience of Clinica is neuroscientists or clinicians conducting clinical neuroscience studies involving multimodal imaging, and researchers developing advanced machine learning algorithms applied to neuroimaging data.
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- 2021
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111. Groupe de Brauer non ramifi\'e d'espaces homog\`enes de tores
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Colliot-Thélène, Jean-Louis
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Mathematics - Algebraic Geometry ,14F22, 11E72, 14G25 - Abstract
Let k be a field, X a smooth, projective k-variety. If X is geometrically rational, there is an injective map from the quotient of Brauer groups Br(X)/Br(k) into the first Galois cohomology group of the lattice given by the geometric Picard group. In this note, where the main attention is on smooth compactifications of homogeneous spaces of algebraic k-tori, we show how under some hypotheses the map is onto, and how one may in some special case exhibit concrete generators in Br(X). This is applied to the analysis of counterexamples to the local-global principle for norms in biquadratic extensions of number fields.
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- 2012
112. Approximation forte en famille
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Colliot-Thélène, Jean-Louis and Harari, David
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Mathematics - Number Theory ,Mathematics - Algebraic Geometry ,11G35, 14G05, 14G25, 11E99, 14F22, 20G35 - Abstract
Let $k$ be a number field and $X$ a smooth integral affine variety equipped with a morphism $f : X \to A^1_k$ to the affine line. Assume that all fibres of $f$ are split, for instance that they are geometrically integral. Assume that the generic fibre of $f$ is a homogeneous space of a simply connected, almost simple, semisimple group $G/k(t)$, and that the geometric stabilizers are connected reductive groups. Let $v$ be a place of $k$ such that the fibration $f$ acquires a rational section over the completion $k_v$ at $v$. Assume moreover that at almost all points $x \in A^1(k_v)$ the specialized group $G_x$ is isotropic over $k_v$. If the Brauer group of $X$ is reduced to the Brauer group of $k$, then strong approximation holds for $X$ away from the place $v$., Comment: (July 16th, 2013) The summary is correct, but as Dasheng Wei pointed out to us, there was a mistake in a proof in the previous versions of the paper. Section 3 has been rewritten. Alongside with a technique from earlier papers by the second named author, a new technical tool is Proposition 3.4, which combines strong approximation with a specific proof of Hilbert's irreducibility theorem
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- 2012
113. Groupe de Brauer non ramifi\'e de quotients par un groupe fini
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Colliot-Thélène, Jean-Louis
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,14F22, 12G05, 14E08, 14M20 - Abstract
Let k be a field, G a finite group embedded in the k-group SL(n). For k an algebraically closed field, Bogomolov gave a formula for the unramified Brauer group of the quotient SL(n)/G. We develop his method over any characteristic zero field. This purely algebraic method enables us to recover and generalize results of Harari and of Demarche over number fields, such as the triviality of the unramified Brauer group for k=Q and G of odd order. --- Soient k un corps et G un groupe fini plong\'e dans le k-groupe SL(n).Pour k alg\'ebriquement clos, Bogomolov a donn\'e une formule pour le groupe de Brauer non ramifi\'e du quotient SL(n)/G. On examine ce que donne sa m\'ethode sur un corps k quelconque (de caract\'eristique nulle). Par cette m\'ethode purement alg\'ebrique, on retrouve et \'etend des r\'esultats obtenus par Harari et par Demarche au moyen de m\'ethodes arithm\'etiques, comme la trivialit\'e du groupe de Brauer non ramifi\'e pour k= Q et G d'ordre impair., Comment: 10 pages, in French
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- 2012
114. Strong approximation for the total space of certain quadric fibrations
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Colliot-Thélène, Jean-Louis and Xu, Fei
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Mathematics - Number Theory ,Mathematics - Algebraic Geometry ,11D99, 11E99, 14G99 - Abstract
We study equations in four variables (x,y,z,t) of the shape q(x,y,z)=P(t), where q(x,y,z) is an indefinite ternary quadratic form over the integers and P(t) is a polynomial in one variable with integral coefficients. If P(t) is not the product of a constant and the square of a polynomial, strong approximation holds for integral solutions (x,y,z,t). In the general case, we show that the integral Brauer-Manin conditions are the only obstructions to strong approximation. We actually study the analogous situation over an arbitrary number field. --- Nous \'etudions les \'equations \`a quatre variables (x,y,z,t) \`a coefficients entiers du type q(x,y,z)=P(t), o\`u q(x,y,z) est une forme quadratique enti\`ere ternaire ind\'efinie sur les r\'eels, et P(t) un polyn\^ome \`a coefficients entiers en une variable. Lorsque le polyn\^ome n'est pas le produit d'une constante et d'un carr\'e de polyn\^ome, nous \'etablissons l'approximation forte pour les solutions de ces \'equations en entiers (x,y,z,t). Dans le cas g\'en\'eral, nous montrons que l'obstruction de Brauer-Manin enti\`ere est la seule obstruction \`a l'approximation forte. Nous \'etudions la situation sur un corps de nombres quelconque., Comment: 26 pages, in English
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- 2011
115. Quelques cas d'annulation du troisi\`eme groupe de cohomologie non ramifi\'ee
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Colliot-Thélène, Jean-Louis
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Mathematics - Algebraic Geometry ,Mathematics - K-Theory and Homology ,14C35, 14E08, 14F99 - Abstract
The third unramified cohomology group is shown to vanish on certain varieties equipped with a pencil of quadrics or of smooth complete intersections of two quadrics. Over the complex field, this shows that the integral Hodge conjecture in degree 4 holds for such varieties. --- On \'etablit la nullit\'e du troisi\`eme groupe de cohomologie non ramifi\'ee pour certaines vari\'et\'es munies d'un pinceau de quadriques ou d'intersections compl\`etes lisses de deux quadriques. Sur les complexes, ceci permet d'\'etablir la conjecture de Hodge enti\`ere en degr\'e 4 pour de telles vari\'et\'es.
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- 2011
116. Sur le groupe de Brauer transcendant
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Colliot-Thélène, Jean-Louis and Skorobogatov, Alexei N.
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Mathematics - Algebraic Geometry ,14F22 (Primary) 14G99, 14C25, 16K50 (Secondary) - Abstract
For a smooth and projective variety X over a field k of characteristic zero we prove the finiteness of the cokernel of the natural map from the Brauer group of X to the Galois-invariant subgroup of the Brauer group of the same variety over an algebraic closure of k. Under further conditions on k, e.g. over number fields, we give estimates for the order of this cokernel. ---- Soit X une vari\'et\'e projective et lisse sur un corps k de caract\'eristique z\'ero. Le groupe de Brauer de X s'envoie dans les invariants, sous le groupe de Galois absolu de k, du groupe de Brauer de la m\^eme vari\'et\'e consid\'er\'ee sur une cl\^oture alg\'ebrique de k. Nous montrons que le quotient est fini. Sous des hypoth\`eses suppl\'ementaires, par exemple sur k un corps de nombres, nous donnons des estimations sur l'ordre de ce quotient., Comment: 33 pages, in French
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- 2011
117. Cycles de codimension 2 et H^3 non ramifi\'e pour les vari\'et\'es sur les corps finis
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Colliot-Thélène, Jean-Louis and Kahn, Bruno
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Mathematics - Algebraic Geometry ,19E15, 14G15, 14G25, 14C25, 14C35 - Abstract
Let $X$ be a smooth projective variety over a finite field $\F$. We discuss the unramified cohomology group $H^3_\nr(X,\Q/\Z(2))$. Several conjectures put together imply that this group is finite. For certain classes of threefolds, $H^3_\nr(X,\Q/\Z(2))$ actually vanishes. It is an open question whether this holds true for arbitrary threefolds. For a threefold $X$ equipped with a fibration onto a curve $C$, the generic fibre of which is a smooth projective surface $V$ over the global field $\F(C)$, the vanishing of $H^3_\nr(X,\Q/\Z(2))$ together with the Tate conjecture for divisors on $X$ implies a local-global principle of Brauer--Manin type for the Chow group of zero-cycles on $V$. This sheds a new light on work started thirty years ago. ----- Soit $X$ une vari\'et\'e projective et lisse sur un corps fini $\F$. On s'int\'eresse au groupe de cohomologie non ramifi\'ee $H^3_\nr(X,\Q/\Z(2))$. Un faisceau de conjectures implique que ce groupe est fini. Pour certaines classes de solides, on a $H^3_\nr(X,\Q/\Z(2))=0$. Savoir si c'est le cas pour tout solide est un probl\`eme ouvert. Lorsqu'un solide $X$ est fibr\'e au-dessus d'une courbe $C$, de fibre g\'en\'erique une surface projective et lisse $V$ sur le corps global $\F(C)$, la combinaison de $H^3_\nr(X,\Q/\Z(2))=0$ et de la conjecture de Tate pour $X$ a pour cons\'equence un principe local-global de type Brauer--Manin pour le groupe de Chow des z\'ero-cycles de la fibre g\'en\'erique $V$. Ceci \'eclaire d'un jour nouveau des investigations commenc\'ees il y a trente ans., Comment: Slightly revised version of arXiv:1104.3350v2 [math.AG]. To appear in the Journal of K-Theory
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- 2011
118. Potential density for some families of homogeneous spaces
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Colliot-Thélène, J. -L. and Iyer, J. N.
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,14C25, 14D05, 14D20, 14D21 - Abstract
For a smooth, projective family of homogeneous varieties defined over a number field, we show that if potential density holds for the rational points of the base, then it also holds for the total space. A conjecture of Campana and Peternell, known in dimension at most 4 and for certain higher dimensional cases, would then imply potential density for the rational points of smooth projective varieties over number fields whose tangent bundle is nef., Comment: 10 p
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- 2011
119. Die Geschichtlichen Grundbegriffe. Allgemeine Einführung
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Catherine Colliot-Thélène and Élisabeth Kauffmann
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Geschichtliche Grundbegriffe ,Koselleck ,Social sciences (General) ,H1-99 - Published
- 2021
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120. Demokratie. Einführung
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Catherine Colliot-Thélène
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démocratie ,Social sciences (General) ,H1-99 - Published
- 2021
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121. Démocratie. Présentation
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Catherine Colliot-Thélène
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démocratie ,Social sciences (General) ,H1-99 - Published
- 2021
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122. Les Geschichtliche Grundbegriffe. Présentation générale
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Catherine Colliot-Thélène and Élisabeth Kauffmann
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Koselleck ,Geschichtliche Grundbegriffe ,Social sciences (General) ,H1-99 - Published
- 2021
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123. Good reduction of the Brauer-Manin obstruction
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Colliot-Thélène, J. -L. and Skorobogatov, A. N.
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Mathematics - Algebraic Geometry ,14F22, 14G05, 11G35, 11G25 - Abstract
For a smooth and projective variety over a number field with torsion free geometric Picard group and finite transcendental Brauer group we show that only the archimedean places, the primes of bad reduction and the primes dividing the order of the transcendental Brauer group can turn up in the description of the Brauer-Manin set., Comment: 17 pages, in English
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- 2010
124. Cohomologie non ramifi\'ee et conjecture de Hodge enti\`ere
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Colliot-Thélène, Jean-Louis and Voisin, Claire
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Mathematics - Algebraic Geometry ,14F20, 14C25, 14C30, 14C35, 19E15 - Abstract
Building upon the Bloch-Kato conjecture in Milnor K-theory, we relate the third unramified cohomology group with Q/Z coefficients with a group which measures the failure of the integral Hodge conjecture in degree 4. As a first consequence, a geometric theorem of the second-named author implies that the third unramified cohomology group with Q/Z coefficients vanishes on all uniruled threefolds. As a second consequence, a 1989 example by Ojanguren and the first named author implies that the integral Hodge conjecture in degree 4 fails for unirational varieties of dimension at least 6. For certain classes of threefolds fibered over a curve, we establish a relation between the integral Hodge conjecture and the computation of the index of the generic fibre. En nous appuyant sur la conjecture de Bloch-Kato en K-th\'eorie de Milnor, nous \'etablissons un lien g\'en\'eral entre le d\'efaut de la conjecture de Hodge enti\`ere pour la cohomologie de degr\'e 4 et le troisi\`eme groupe de cohomologie non ramifi\'e \`a coefficients Q/Z. Ceci permet de montrer que sur un solide unir\'egl\'e le troisi\`eme groupe de cohomologie non ramifi\'e \`a coefficients Q/Z s'annule, ce que la K-th\'eorie alg\'ebrique ne permet d'obtenir que dans certains cas. Ceci permet \`a l'inverse de d\'eduire d'exemples ayant leur source en K-th\'eorie que la conjecture de Hodge enti\`ere pour la cohomologie de degr\'e 4 peut \^etre en d\'efaut pour les vari\'et\'es rationnellement connexes. Pour certaines familles \`a un param\`etre de surfaces, on \'etablit un lien entre la conjecture de Hodge enti\`ere et l'indice de la fibre g\'en\'erique., Comment: Final version, 48 pages, to appear in Duke Mathematical Journal
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- 2010
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125. Zero-cycles and rational points on some surfaces over a global function field
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Colliot-Thélène, Jean-Louis and Swinnerton-Dyer, Sir Peter
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,14G25 14G15 14G05 14C25 11D25 - Abstract
Let F be a finite field of characteristic p. We consider smooth surfaces over F(t) defined by an equation f+tg=0, where f and g are forms of degree d in 4 variables with coefficients in F, with d prime to p. We prove : For such surfaces over F(t), the Brauer-Manin obstruction to the existence of a zero-cycle of degree one is the only obstruction. For d=3 (cubic surfaces), this leads to the same result for rational points. -- Soit F un corps fini de caract\'eristique p. Pour une surface lisse sur F(t) d\'efinie par une \'equation f+tg=0, o\`u f et g sont deux formes de degr\'e d sur F en 4 variables, avec d premier \`a p, nous montrons que l'obstruction de Brauer-Manin au principe de Hasse pour les z\'ero-cycles de degr\'e 1 est la seule obstruction. Pour d=3 (surfaces cubiques), on en d\'eduit le m\^{e}me \'enonc\'e pour les points rationnels., Comment: The title has changed and the text has been split into sections. In the statement of Theorems 1 and 3, "degree prime to char(F)" was corrected to "degree a power of char(F)."
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- 2010
126. Groupe de Chow des z\'ero-cycles sur les vari\'et\'es p-adiques
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Colliot-Thélène, J. -L.
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,11G25, 14C25, 14G20, 14C35 - Abstract
Ceci est un rapport sur l'article "A finiteness theorem for zero-cycles over p-adic fields" (arXiv:math/0605165) de Shuji Saito et Kanetomo Sato. ----- This is a survey on the paper "A finiteness theorem for zero-cycles over p-adic fields" (arXiv:math/0605165) by Shuji Saito and Kanetomo Sato., Comment: 29 pages, Expos\'e au S\'eminaire Bourbaki (14 Novembre 2009)
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- 2010
127. Une version du th\'eor\`eme d'Amer et Brumer pour les z\'ero-cycles
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Colliot-Thélène, J. -L. and Levine, Marc
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Mathematics - Algebraic Geometry ,14C25 - Abstract
M. Amer and A. Brumer have shown that, for two homogeneous quadratic polynomials f and g in at least 3 variables over a field k of characteristic different from 2, the locus f=g=0 has non-trivial solution over k if and only if, for a variable t, the equation f+tg=0 has a non-trivial solution over k(t). We consider a modified version of this result, and show that the projective variety over k defined by f_0=...=f_r=0, where the f_i are homogeneous polynomials over k of the same degree d\ge2 in n+1 variables (with n+1\ge r+2) , has a 0-cycle of degree 1 over k if and only if the generic hypersurface f_0+t_1f_1+...+t_rf_r=0 has a 0-cycle of degree 1 over k(t_1,...,t_r)., Comment: revised final version. 8 pages (originally 6 pages)
- Published
- 2009
128. Groupe de Brauer et points entiers de deux familles de surfaces cubiques affines
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Colliot-Thélène, Jean-Louis and Wittenberg, Olivier
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Mathematics - Number Theory ,Mathematics - Algebraic Geometry - Abstract
Let a be a nonzero integer. If a is not congruent to 4 or 5 modulo 9 then there is no Brauer-Manin obstruction to the existence of integers x, y, z such that x^3+y^3+z^3=a. In addition, there is no Brauer-Manin obstruction to the existence of integers x, y, z such that x^3+y^3+2z^3=a., Comment: 24 pages; minor changes only
- Published
- 2009
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129. Autour de la conjecture de Tate `a coefficients Z_l pour les vari'et'es sur les corps finis
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Colliot-Thélène, Jean-Louis and Szamuely, Tamás
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,14C25, 14G15 - Abstract
This partly expository paper investigates versions of the Tate conjecture on the cycle map for varieties defined over finite fields with values in 'etale cohomology with Z_\ell-coefficients. The bulk of the paper is an exposition of a 1998 result of C. Schoen which shows that an integral version of the conjecture holds for 1-cycles provided the usual conjecture is true for divisors on surfaces. In a last section we then derive from Schoen's theorem new results on the existence of degree one zero-cycles on varieties defined over the function field of a smooth proper curve C over the algebraic closure of a finite field. In particular, we show that if the variety in question is a smooth projective complete intersection of dimension at least 3 and of degree prime to the characteristic, then a zero-cycle of degree one exists if the Tate conjecture is true for divisors on surfaces and the variety extends to a proper fibration over C all of whose fibres possess a component of multiplicity one., Comment: 16 pages, to appear in proceedings of Columbus conference on algebraic cycles (Clay Institute Publications) v2: Discussion of Atiyah-Hirzebruch counterexample added, following suggestions of Burt Totaro
- Published
- 2009
130. Is the function field of a reductive Lie algebra purely transcendental over the field of invariants for the adjoint action?
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Colliot-Thélène, Jean-Louis, Kunyavskiĭ, Boris, Popov, Vladimir L., and Reichstein, Zinovy
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Mathematics - Algebraic Geometry ,Mathematics - Group Theory ,14E08, 17B45, 14L30, 20C10, 14F22 - Abstract
Let $k$ be a field of characteristic zero, let $G$ be a connected reductive algebraic group over $k$ and let $\mathfrak{g}$ be its Lie algebra. Let $k(G)$, respectively, $k(\mathfrak{g})$, be the field of $k$-rational functions on $G$, respectively, $\mathfrak{g}$. The conjugation action of $G$ on itself induces the adjoint action of $G$ on $\mathfrak{g}$. We investigate the question whether or not the field extensions $k(G)/k(G)^G$ and $k(\mathfrak{g})/k(\mathfrak{g})^G$ are purely transcendental. We show that the answer is the same for $k(G)/k(G)^G$ and $k(\mathfrak{g})/k(\mathfrak{g})^G$, and reduce the problem to the case where $G$ is simple. For simple groups we show that the answer is positive if $G$ is split of type ${\sf A}_{n}$ or ${\sf C}_n$, and negative for groups of other types, except possibly ${\sf G}_{2}$. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of $G$ on itself. The results and methods of this paper have played an important part in recent A. Premet's negative solution (arxiv:0907.2500) of the Gelfand--Kirillov conjecture for finite-dimensional simple Lie algebras of every type, other than ${\sf A}_n$, ${\sf C}_n$, and ${\sf G}_2$., Comment: Final version, 37 pages. To appear in Compositio Mathematica.
- Published
- 2009
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131. Patching and local-global principles for homogeneous spaces over function fields of p-adic curves
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Colliot-Thélène, J. -L., Parimala, R., and Suresh, V.
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,11G99, 14G99, 14G05, 11E72, 11E12, 20G35 - Abstract
This is the final version, to appear in Commentarii Mathematici Helvetici., Comment: 17 pages, in English
- Published
- 2008
132. Vari'et'es presque rationnelles, leurs points rationnels et leurs d'eg'en'erescences
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Colliot-Thélène, J-L.
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,14G05, 14D06, 14M20, 14G99, 14E99 - Abstract
This survey, which contains very few proofs, addresses the general question: Over a given type of field, is there a natural class of varieties which automatically have a rational point? Fields under consideration here include: finite fields, p-adic fields, function fields in one or two variables over an algebraically closed field. Classical answers are given by the Chevalley-Warning theorem and by Tsen's theorem. More general answers were provided by a theorem of Graber, Harris and Starr and by a theorem of Esnault. The latter results apply to rationally connected varieties. We discuss these varieties from various angles : weak approximation, R-equivalence, Chow group of zero-cycles. Ongoing work on `rationally simply connected' varieties over function fields in two variables is also mentioned. A common thread in this report is the study of the special fibre of a scheme over a discrete valuation ring: if the generic fibre has a simple geometry, what does it imply for the special fibre?, Comment: Lecture notes for a CIME summer school (Cetraro, September 2007), 56 pages, in French
- Published
- 2008
133. Remarques sur un article r'ecent de B. Poonen
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Colliot-Thélène, J-L.
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Mathematics - Number Theory ,Mathematics - Algebraic Geometry ,14G05 ,14G25 ,11G35 ,14J20 ,14F22 - Abstract
B. Poonen recently produced smooth threefolds over a number field which do not have a rational point but have no Brauer-Manin obstruction even after descent to a finite 'etale cover. In this note I show that the varieties he produces have zero-cycles of degree 1. ----- B. Poonen a r'ecemment exhib'e des exemples de vari'et'es projectives et lisses de dimension 3 sur un corps de nombres qui n'ont pas de point rationnel et pour lesquelles il n'y a pas d'obstruction de Brauer-Manin apr`es rev^etement fini 'etale. Dans cette note, je montre que les vari'et'es qu'il construit poss`edent des z'ero-cycles de degr'e 1., Comment: 8 pages
- Published
- 2008
134. Disrupted core-periphery structure of multimodal brain networks in Alzheimer’s disease
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Jeremy Guillon, Mario Chavez, Federico Battiston, Yohan Attal, Valentina La Corte, Michel Thiebaut de Schotten, Bruno Dubois, Denis Schwartz, Olivier Colliot, and Fabrizio De Vico Fallani
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Neurodegenerative diseases ,Brain connectivity ,Multilayer network theory ,MEG ,DWI ,fMRI ,Neurosciences. Biological psychiatry. Neuropsychiatry ,RC321-571 - Abstract
In Alzheimer’s disease (AD), the progressive atrophy leads to aberrant network reconfigurations both at structural and functional levels. In such network reorganization, the core and peripheral nodes appear to be crucial for the prediction of clinical outcome because of their ability to influence large-scale functional integration. However, the role of the different types of brain connectivity in such prediction still remains unclear. Using a multiplex network approach we integrated information from DWI, fMRI, and MEG brain connectivity to extract an enriched description of the core-periphery structure in a group of AD patients and age-matched controls. Globally, the regional coreness—that is, the probability of a region to be in the multiplex core—significantly decreased in AD patients as result of a random disconnection process initiated by the neurodegeneration. Locally, the most impacted areas were in the core of the network—including temporal, parietal, and occipital areas—while we reported compensatory increments for the peripheral regions in the sensorimotor system. Furthermore, these network changes significantly predicted the cognitive and memory impairment of patients. Taken together these results indicate that a more accurate description of neurodegenerative diseases can be obtained from the multimodal integration of neuroimaging-derived network data. Alzheimer’s disease includes a progressive destruction of axonal pathways leading to global network changes. While these changes affect both the anatomy and the function of the brain, a joint characterization of the impact on the nodes of the network is still lacking. By integrating information from multiple neuroimaging data, within a modern complex systems framework, we show that the nodes constituting the core of the brain network are the most impacted by the disconnection process. Furthermore, these network alterations significantly predict the cognitive and memory impairment of patients and represent potential biomarkers of disease progression. We posit that a more accurate description of neurodegenerative diseases can be obtained by analyzing and modeling brain networks derived from multimodal neuroimaging data.
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- 2019
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135. Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms
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Colliot-Thélène, Jean-Louis and Xu, Fei
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Mathematics - Number Theory ,Mathematics - Algebraic Geometry ,11G99, 14G99, 11E12, 20G35, 14F22 - Abstract
An integer may be represented by a quadratic form over each ring of p-adic integers and over the reals without being represented by this quadratic form over the integers. More generally, such failure of a local-global principle may occur for the representation of one integral quadratic form by another integral quadratic form. We show that many such examples may be accounted for by a Brauer-Manin obstruction for the existence of integral points on schemes defined over the integers. For several types of homogeneous spaces of linear algebraic groups, this obstruction is shown to be the only obstruction to the existence of integral points. ----- Une forme quadratique enti\`ere peut \^etre repr\'esent\'ee par une autre forme quadratique enti\`ere sur tous les anneaux d'entiers p-adiques et sur les r\'eels, sans l'\^etre sur les entiers. On en trouve de nombreux exemples dans la litt\'erature. Nous montrons qu'une partie de ces exemples s'explique au moyen d'une obstruction de type Brauer-Manin pour les points entiers. Pour plusieurs types d'espaces homog\`enes de groupes alg\'ebriques lin\'eaires, cette obstruction est la seule obstruction \`a l'existence d'un point entier., Comment: 53 pages, in English
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- 2007
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136. Rational surfaces and canonical dimension of PGL_6
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Colliot-Thélène, Jean-Louis, Karpenko, Nikita A., and Merkurjev, Alexander S.
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Mathematics - Algebraic Geometry ,20G15 ,14J26 - Abstract
The "canonical dimension" of an algebraic group over a field by definition is the maximum of the canonical dimensions of principal homogenous spaces under that group. Over a field of characteristic zero, we prove that the canonical dimension of the projective linear group PGL_6 is 3. We give two distinct proofs, both of which rely on the birational classification of rational surfaces over a nonclosed field. One of the proofs involves taking a novel look at del Pezzo surfaces of degree 6.
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- 2006
137. The elementary obstruction and homogeneous spaces
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Borovoi, M., Colliot-Thélène, J-L., and Skorobogatov, A. N.
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Mathematics - Number Theory ,Mathematics - Algebraic Geometry ,14G05, 11G99, 12G05 - Abstract
Let $k$ be a field of characteristic zero and ${\bar k}$ an algebraic closure of $k$. For a geometrically integral variety $X$ over $k$, we write ${\bar k}(X)$ for the function field of ${\bar X}=X\times_k{\bar k}$. If $X$ has a smooth $k$-point, the natural embedding of multiplicative groups ${\bar k}^*\hookrightarrow {\bar k}(X)^* $ admits a Galois-equivariant retraction. In the first part of the paper, over local and then over global fields, equivalent conditions to the existence of such a retraction are given. They are expressed in terms of the Brauer group of $X$. In the second part of the paper, we restrict attention to varieties which are homogeneous spaces of connected but otherwise arbitrary algebraic groups, with connected geometric stabilizers. For $k$ local or global, for such a variety $X$, in many situations but not all, the existence of a Galois-equivariant retraction to ${\bar k}^*\hookrightarrow {\bar k}(X)^* $ ensures the existence of a $k$-rational point on $X$. For homogeneous spaces of linear algebraic groups, the technique also handles the case where $k$ is the function field of a complex surface., Comment: To appear in Duke Mathematical Journal. An appendix on the Brauer-Manin obstruction for homogeneous spaces has been added
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- 2006
138. Quelques questions d'approximation faible pour les tores alg\'ebriques
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Colliot-Thélène, J-L. and Suresh, V.
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Mathematics - Number Theory ,Mathematics - Algebraic Geometry ,20G30, 20G25, 14G40, 11E72, 14M25 - Abstract
Let K be a global field, T a K-torus and S a finite set of places of K. Let K_v be the completion at a place v. Denote by T(O_v) the maximal compact subgroup of the group T(K_v) of K_v-points of T. We show that the diagonal map from T(K) to the product for v in S of the T(K_v)/T(O_v) need not be onto. As a corollary, for suitable v, the group T(O_v) does not cover all R-equivalence classes in T(K_v). While studying the height zeta functions of an algebraic torus over a function field in one variable over a finite field, D. Bourqui showed that Peyre's constant from the number field case should be multiplied by an integer. The same type of torus as constructed for the above problem enables us to show that this integer need not always be 1. ----- Soient K un corps global, T un K-tore, S un ensemble fini de places de K. On note K_v le compl\'et\'e de K en une place v. Soit T(K), resp. T(K_v), le groupe des points K-rationnels, resp. K_v-rationnels, de T. Notons T(O_v) le sous-groupe compact maximal de T(K_v). Nous montrons que pour T et S convenables l'application diagonale de T(K) vers le produit pour v dans S des T(K_v)/T(O_v) n'est pas surjective. Cela implique que pour v convenable le groupe T(O_v) ne couvre pas forc\'ement toutes les classes de R-\'equivalence de T(K_v). Lorsque K est un corps de fonctions d'une variable sur un corps fini, en utilisant le m\^eme type de tore, nous montrons que le facteur suppl\'ementaire par lequel D. Bourqui doit, lors son \'etude de la fonction z\^eta des hauteurs des vari\'et\'es toriques, multiplier la constante de Peyre, n'est pas toujours \'egal \`a 1., Comment: 12 pages, in French, to appear in Annales de l'institut Fourier
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- 2006
139. Fields of cohomological dimension one versus C_1-fields
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Colliot-Thélène, Jean-Louis
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Mathematics - Algebraic Geometry ,Mathematics - K-Theory and Homology ,14G05, 12G10, 14C35 ,14J26, 11E76 - Abstract
Ax gave examples of fields of cohomological dimension 1 which are not C_1-fields. Kato and Kuzumaki asked whether a weak form of the C_1-property holds for all fields of cohomological dimension 1 (existence of solutions in extensions of coprime degree rather than existence of a solution in the ground field). Using work of Merkur'ev and Suslin, and of Rost, D. Madore and I produced examples which show that the answer is in the negative. In the present note, I produce examples which require less work than the original ones. In the original paper, some of the examples were given by forms of degree 3 in 4 variables. Here, for an arbitrary prime p>3, I use forms of degree p in p+1 variables., Comment: 5 pages, in English
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- 2005
140. Un th\'eor\`eme de finitude pour le groupe de Chow des z\'ero-cycles d'un groupe alg\'ebrique lin\'eaire sur un corps p-adique
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Colliot-Thélène, Jean-Louis
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Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,14C15 ,11E72, 11G25, 14G20, 20G25 - Abstract
Let X be a smooth compactification of a connected linear algebraic group over a field k. The Chow group of degree nought zero-cycles on X is a torsion group. When k is a p-adic field, we show that the prime-to-p component of this group is finite. ----- Sei X eine glatte Kompaktifizierung einer zusammenhaengenden linearen Gruppe ueber einem Koerper k. Die Chowgruppe der nulldimensionalen Zyklen von X vom Grad Null ist eine Torsionsgruppe. Wir zeigen : wenn k ein p-adischer Koerper ist, dann ist der prim-zu-p Anteil dieser Gruppe endlich., Comment: 14 pages, in French, with a German summary. To appear in Inventiones mathematicae
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- 2005
141. Differential early subcortical involvement in genetic FTD within the GENFI cohort
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Martina Bocchetta, Emily G. Todd, Georgia Peakman, David M. Cash, Rhian S. Convery, Lucy L. Russell, David L. Thomas, Juan Eugenio Iglesias, John C. van Swieten, Lize C. Jiskoot, Harro Seelaar, Barbara Borroni, Daniela Galimberti, Raquel Sanchez-Valle, Robert Laforce, Fermin Moreno, Matthis Synofzik, Caroline Graff, Mario Masellis, Maria Carmela Tartaglia, James B. Rowe, Rik Vandenberghe, Elizabeth Finger, Fabrizio Tagliavini, Alexandre de Mendonça, Isabel Santana, Chris R. Butler, Simon Ducharme, Alexander Gerhard, Adrian Danek, Johannes Levin, Markus Otto, Sandro Sorbi, Isabelle Le Ber, Florence Pasquier, Jonathan D. Rohrer, Sónia Afonso, Maria Rosario Almeida, Sarah Anderl-Straub, Christin Andersson, Anna Antonell, Silvana Archetti, Andrea Arighi, Mircea Balasa, Myriam Barandiaran, Nuria Bargalló, Robart Bartha, Benjamin Bender, Alberto Benussi, Maxime Bertoux, Anne Bertrand, Valentina Bessi, Sandra Black, Sergi Borrego-Ecija, Jose Bras, Alexis Brice, Rose Bruffaerts, Agnès Camuzat, Marta Cañada, Valentina Cantoni, Paola Caroppo, Miguel Castelo-Branco, Olivier Colliot, Thomas Cope, Vincent Deramecourt, María de Arriba, Giuseppe Di Fede, Alina Díez, Diana Duro, Chiara Fenoglio, Camilla Ferrari, Catarina B. Ferreira, Nick Fox, Morris Freedman, Giorgio Fumagalli, Aurélie Funkiewiez, Alazne Gabilondo, Roberto Gasparotti, Serge Gauthier, Stefano Gazzina, Giorgio Giaccone, Ana Gorostidi, Caroline Greaves, Rita Guerreiro, Carolin Heller, Tobias Hoegen, Begoña Indakoetxea, Vesna Jelic, Hans-Otto Karnath, Ron Keren, Gregory Kuchcinski, Tobias Langheinrich, Thibaud Lebouvier, Maria João Leitão, Albert Lladó, Gemma Lombardi, Sandra Loosli, Carolina Maruta, Simon Mead, Lieke Meeter, Gabriel Miltenberger, Rick van Minkelen, Sara Mitchell, Katrina Moore, Benedetta Nacmias, Annabel Nelson, Jennifer Nicholas, Linn Öijerstedt, Jaume Olives, Sebastien Ourselin, Alessandro Padovani, Jessica Panman, Janne M. Papma, Yolande Pijnenburg, Cristina Polito, Enrico Premi, Sara Prioni, Catharina Prix, Rosa Rademakers, Veronica Redaelli, Daisy Rinaldi, Tim Rittman, Ekaterina Rogaeva, Adeline Rollin, Pedro Rosa-Neto, Giacomina Rossi, Martin Rossor, Beatriz Santiago, Dario Saracino, Sabrina Sayah, Elio Scarpini, Sonja Schönecker, Elisa Semler, Rachelle Shafei, Christen Shoesmith, Imogen Swift, Miguel Tábuas-Pereira, Mikel Tainta, Ricardo Taipa, David Tang-Wai, Paul Thompson, Hakan Thonberg, Carolyn Timberlake, Pietro Tiraboschi, Philip Van Damme, Mathieu Vandenbulcke, Michele Veldsman, Ana Verdelho, Jorge Villanua, Jason Warren, Carlo Wilke, Ione Woollacott, Elisabeth Wlasich, Henrik Zetterberg, and Miren Zulaica
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Genetic frontotemporal dementia ,MRI imaging ,Brain volumetry ,Presymptomatic stage ,Computer applications to medicine. Medical informatics ,R858-859.7 ,Neurology. Diseases of the nervous system ,RC346-429 - Abstract
Background: Studies have previously shown evidence for presymptomatic cortical atrophy in genetic FTD. Whilst initial investigations have also identified early deep grey matter volume loss, little is known about the extent of subcortical involvement, particularly within subregions, and how this differs between genetic groups. Methods: 480 mutation carriers from the Genetic FTD Initiative (GENFI) were included (198 GRN, 202 C9orf72, 80 MAPT), together with 298 non-carrier cognitively normal controls. Cortical and subcortical volumes of interest were generated using automated parcellation methods on volumetric 3 T T1-weighted MRI scans. Mutation carriers were divided into three disease stages based on their global CDR® plus NACC FTLD score: asymptomatic (0), possibly or mildly symptomatic (0.5) and fully symptomatic (1 or more). Results: In all three groups, subcortical involvement was seen at the CDR 0.5 stage prior to phenoconversion, whereas in the C9orf72 and MAPT mutation carriers there was also involvement at the CDR 0 stage. In the C9orf72 expansion carriers the earliest volume changes were in thalamic subnuclei (particularly pulvinar and lateral geniculate, 9–10%) cerebellum (lobules VIIa-Crus II and VIIIb, 2–3%), hippocampus (particularly presubiculum and CA1, 2–3%), amygdala (all subregions, 2–6%) and hypothalamus (superior tuberal region, 1%). In MAPT mutation carriers changes were seen at CDR 0 in the hippocampus (subiculum, presubiculum and tail, 3–4%) and amygdala (accessory basal and superficial nuclei, 2–4%). GRN mutation carriers showed subcortical differences at CDR 0.5 in the presubiculum of the hippocampus (8%). Conclusions: C9orf72 expansion carriers show the earliest and most widespread changes including the thalamus, basal ganglia and medial temporal lobe. By investigating individual subregions, changes can also be seen at CDR 0 in MAPT mutation carriers within the limbic system. Our results suggest that subcortical brain volumes may be used as markers of neurodegeneration even prior to the onset of prodromal symptoms.
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- 2021
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142. The density of rational points in curves and surfaces
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Heath-Brown, D. R. and Colliot-Thélène, J. -L.
- Subjects
Mathematics - Number Theory - Abstract
Let $X$ be an algebraic variety, defined over the rationals. This paper gives upper bounds for the number of rational points on $X$, with height at most $B$, for the case in which $X$ is a curve or a surface. In the latter case one excludes from the counting function those points that lie on lines in the surface. The bounds are uniform for all $X$ of a given degree. They are best possible in the case of curves. As an application it is shown that if $F$ is an irreducible binary form of degree 3 or more then almost all integers represented by $F$ have essentially one such representation., Comment: 46 pages, published version; appendix by J.-L. Colliot-Th\'el\`ene
- Published
- 2004
143. Ensemble Learning of Convolutional Neural Network, Support Vector Machine, and Best Linear Unbiased Predictor for Brain Age Prediction: ARAMIS Contribution to the Predictive Analytics Competition 2019 Challenge
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Baptiste Couvy-Duchesne, Johann Faouzi, Benoît Martin, Elina Thibeau–Sutre, Adam Wild, Manon Ansart, Stanley Durrleman, Didier Dormont, Ninon Burgos, and Olivier Colliot
- Subjects
brain age ,MRI ,machine learning ,deep learning ,statistical learning ,ensemble learning ,Psychiatry ,RC435-571 - Abstract
We ranked third in the Predictive Analytics Competition (PAC) 2019 challenge by achieving a mean absolute error (MAE) of 3.33 years in predicting age from T1-weighted MRI brain images. Our approach combined seven algorithms that allow generating predictions when the number of features exceeds the number of observations, in particular, two versions of best linear unbiased predictor (BLUP), support vector machine (SVM), two shallow convolutional neural networks (CNNs), and the famous ResNet and Inception V1. Ensemble learning was derived from estimating weights via linear regression in a hold-out subset of the training sample. We further evaluated and identified factors that could influence prediction accuracy: choice of algorithm, ensemble learning, and features used as input/MRI image processing. Our prediction error was correlated with age, and absolute error was greater for older participants, suggesting to increase the training sample for this subgroup. Our results may be used to guide researchers to build age predictors on healthy individuals, which can be used in research and in the clinics as non-specific predictors of disease status.
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- 2020
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144. Predicting PET-derived myelin content from multisequence MRI for individual longitudinal analysis in multiple sclerosis
- Author
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Wen Wei, Emilie Poirion, Benedetta Bodini, Matteo Tonietto, Stanley Durrleman, Olivier Colliot, Bruno Stankoff, and Nicholas Ayache
- Subjects
Conditional GANs ,Attention mechanism ,PET imaging ,Multisequence MRI ,Demyelination and remyelination ,Deep learning ,Neurosciences. Biological psychiatry. Neuropsychiatry ,RC321-571 - Abstract
Multiple sclerosis (MS) is a demyelinating and inflammatory disease of the central nervous system (CNS). The demyelination process can be repaired by the generation of a new sheath of myelin around the axon, a process termed remyelination. In MS patients, the demyelination–remyelination cycles are highly dynamic. Over the years, magnetic resonance imaging (MRI) has been increasingly used in the diagnosis of MS and it is currently the most useful paraclinical tool to assess this diagnosis. However, conventional MRI pulse sequences are not specific for pathological mechanisms such as demyelination and remyelination. Recently, positron emission tomography (PET) with radiotracer [11C]PIB has become a promising tool to measure in-vivo myelin content changes which is essential to push forward our understanding of mechanisms involved in the pathology of MS, and to monitor individual patients in the context of clinical trials focused on repair therapies. However, PET imaging is invasive due to the injection of a radioactive tracer. Moreover, it is an expensive imaging test and not offered in the majority of medical centers in the world. In this work, by using multisequence MRI, we thus propose a method to predict the parametric map of [11C]PIB PET, from which we derived the myelin content changes in a longitudinal analysis of patients with MS. The method is based on the proposed conditional flexible self-attention GAN (CF-SAGAN) which is specifically adjusted for high-dimensional medical images and able to capture the relationships between the spatially separated lesional regions during the image synthesis process. Jointly applying the sketch-refinement process and the proposed attention regularization that focuses on the MS lesions, our approach is shown to outperform the state-of-the-art methods qualitatively and quantitatively. Specifically, our method demonstrated a superior performance for the prediction of myelin content at voxel-wise level. More important, our method for the prediction of myelin content changes in patients with MS shows similar clinical correlations to the PET-derived gold standard indicating the potential for clinical management of patients with MS.
- Published
- 2020
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145. Surfaces de del Pezzo sans point rationnel sur un corps de dimension cohomologique un
- Author
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Colliot-Thelene, Jean-Louis and Madore, David A.
- Subjects
Mathematics - Number Theory ,Mathematics - Algebraic Geometry ,14G05, 12G10, 14C35 (Primary) 14J26, 11E76, 11D09 (Secondary) - Abstract
For each integer d=2,3,4, there exists a field F with cohomological dimension 1 and a del Pezzo surface of degree d over F having no rational point. Proofs use the theorem of Merkur'ev and Suslin, the Riemann-Roch theorem on a surface and Rost's degree formula. ----- Pour chaque entier d=2,3,4, il existe un corps F de dimension cohomologique 1 et une surface de del Pezzo de degre d sur F sans point rationnel. Les demonstrations utilisent le theoreme de Merkur'ev et Suslin, le theoreme de Riemann-Roch sur une surface et la formule du degre de Rost., Comment: 21 pages, in French; to appear in the Journal de l'Institut Mathematique de Jussieu; second version adds a new section refining earlier results
- Published
- 2003
146. Asking students to be active learners: the effects of totally or partially self-generating a graphic organizer on students’ learning performances
- Author
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Colliot, Tiphaine and Jamet, Éric
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- 2019
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147. Understanding the effects of a teacher video on learning from a multimedia document: an eye-tracking study
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Colliot, Tiphaine and Jamet, Éric
- Published
- 2018
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148. Rational connectedness and Galois covers of the projective line
- Author
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Colliot-Thelene, Jean-Louis
- Subjects
Mathematics - Algebraic Geometry ,14Gxx (11Gxx 14Fxx) - Abstract
Let k be a p-adic field. Some time ago, D. Harbater [9] proved that any finite group G may be realized as a regular Galois group over the rational function field in one variable k(t), namely there exists a finite field extension $F/k(t)$, Galois with group G, such that F is a regular extension of k (i.e. k is algebraically closed in F). Moreover, one may arrange that a given k-place of k(t) be totally split in F. Harbater proved this theorem for k an arbitrary complete valued field. Rather formal arguments ([10, \S 4.5]; \S2 hereafter) then imply that the theorem holds over any `large' field k. This in turn is a special case of a result of Pop [15], hence will be referred to as the Harbater/Pop theorem. We refer to [10], [16], [6] for precise references to the literature (work of D\`ebes, Deschamps, Fried, Haran, Harbater, Jarden, Liu, Pop, Serre, and V\"olklein). Most proofs (see [10], [19, 8.4.4, p.~93] and Liu's contribution to [16]; see however [15]) first use direct arguments to establish the theorem when G is a cyclic group (here the nature of the ground field is irrelevant), then proceed by patching, using either formal or rigid geometry, together with GAGA theorems. In the present paper, where I take the case of algebraically closed fields for granted, I show how a technique recently developed by Koll\'ar [12] may be used to give a quite different proof of the Harbater/Pop theorem, when the `large' field k has characteristic zero. This proof actually gives more than the original result (see comment after statement of Theorem 1)., Comment: 15 pages
- Published
- 2000
149. Genome wide association study of incomplete hippocampal inversion in adolescents.
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Claire Cury, Marzia Antonella Scelsi, Roberto Toro, Vincent Frouin, Eric Artiges, Antoine Grigis, Andreas Heinz, Hervé Lemaître, Jean-Luc Martinot, Jean-Baptiste Poline, Michael N Smolka, Henrik Walter, Gunter Schumann, Andre Altmann, Olivier Colliot, and IMAGEN Consortium
- Subjects
Medicine ,Science - Abstract
Incomplete hippocampal inversion (IHI), also called hippocampal malrotation, is an atypical presentation of the hippocampus present in about 20% of healthy individuals. Here we conducted the first genome-wide association study (GWAS) in IHI to elucidate the genetic underpinnings that may contribute to the incomplete inversion during brain development. A total of 1381 subjects contributed to the discovery cohort obtained from the IMAGEN database. The incidence rate of IHI was 26.1%. Loci with P
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- 2020
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150. Comparison and validation of seven white matter hyperintensities segmentation software in elderly patients
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Quentin Vanderbecq, Eric Xu, Sebastian Ströer, Baptiste Couvy-Duchesne, Mauricio Diaz Melo, Didier Dormont, and Olivier Colliot
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White matter hyperintensity ,Dementia ,Artificial intelligence ,Segmentation ,Microvascular ,Computer applications to medicine. Medical informatics ,R858-859.7 ,Neurology. Diseases of the nervous system ,RC346-429 - Abstract
Background: Manual segmentation is currently the gold standard to assess white matter hyperintensities (WMH), but it is time consuming and subject to intra and inter-operator variability. Purpose: To compare automatic methods to segment white matter hyperintensities (WMH) in the elderly in order to assist radiologist and researchers in selecting the most relevant method for application on clinical or research data. Material and Methods: We studied a research dataset composed of 147 patients, including 97 patients from the Alzheimer's Disease Neuroimaging Initiative (ADNI) 2 database and 50 patients from ADNI 3 and a clinical routine dataset comprising 60 patients referred for cognitive impairment at the Pitié-Salpêtrière hospital (imaged using four different MRI machines). We used manual segmentation as the gold standard reference. Both manual and automatic segmentations were performed using FLAIR MRI. We compared seven freely available methods that produce segmentation mask and are usable by a radiologist without a strong knowledge of computer programming: LGA (Schmidt et al., 2012), LPA (Schmidt, 2017), BIANCA (Griffanti et al., 2016), UBO detector (Jiang et al., 2018), W2MHS (Ithapu et al., 2014), nicMSlesion (with and without retraining) (Valverde et al., 2019, 2017). The primary outcome for assessing segmentation accuracy was the Dice similarity coefficient (DSC) between the manual and the automatic segmentation software. Secondary outcomes included five other metrics. Results: A deep learning approach, NicMSlesion, retrained on data from the research dataset ADNI, performed best on this research dataset (DSC: 0.595) and its DSC was significantly higher than that of all others. However, it ranked fifth on the clinical routine dataset and its performance severely dropped on data with artifacts. On the clinical routine dataset, the three top-ranked methods were LPA, SLS and BIANCA. Their performance did not differ significantly but was significantly higher than that of other methods. Conclusion: This work provides an objective comparison of methods for WMH segmentation. Results can be used by radiologists to select a tool.
- Published
- 2020
- Full Text
- View/download PDF
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