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Your search keyword '"Mathematics - Commutative Algebra"' showing total 5 results
Start Over Descriptor "Mathematics - Commutative Algebra" Topic algebraic geometry (math.ag) Language french
5 results on '"Mathematics - Commutative Algebra"'

1. Une construction d'extensions faiblement non ramifiées d'un anneau de valuation

Author

Moret-Bailly, Laurent, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France, Centre Henri Lebesgue, programme ANR-11-LABX-0020-0, ANR-15-CE40-0012,GéoLie,Méthodes géométriques en théorie de Lie(2015), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST, AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-INSTITUT AGRO Agrocampus Ouest

Subjects
Algebra and Number Theory, [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC], MSC: 13F30, 12J10, Commutative Algebra (math.AC), Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry, 13F30, 12J10, FOS: Mathematics, separable field extension, weakly unramified extension, Geometry and Topology, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Valuation ring, Algebraic Geometry (math.AG), Mathematical Physics, Analysis
Abstract

\'Etant donn\'e un anneau de valuation $V$, de corps r\'esiduel $F$ et de groupe des valeurs $\Gamma$, on donne une condition suffisante pour qu'un anneau local dominant $V$ soit un anneau de valuation de groupe $\Gamma$. Lorsque $V$ contient un corps $k$, ce r\'esultat est appliqu\'e \`a la construction d'un anneau de valuation contenant $V$ et une extension donn\'ee $k'$ de $k$, de groupe $\Gamma$ et de corps r\'esiduel engendr\'e par $k'$ et $F$. Cela s'av\`ere possible, notamment, lorsque $k'$ ou $F$ est s\'eparable sur $k$. Given a valuation ring $V$, with residue field $F$ and value group $\Gamma$, we give a sufficient condition for a local ring dominating $V$ to be a valuation ring with the same value group. When $V$ contains a field $k$, we apply this result to the problem of constructing a valuation ring $W$ containing $V$ and a prescribed extension $k'$ of $k$, with value group $\Gamma$ and residue field generated by $k'$ and $F$; this is possible in particular when either $k'$ or $F$ is separable over $k$., Comment: 11 pages, in French. Published in Rend. Sem. Mat. Univ. Padova (Online first)

Published
2022

2. AUGMENTED VALUATION AND MINIMAL PAIR

Author

Vaquié, Michel, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Computer Science::Computer Science and Game Theory, Mathematics::Commutative Algebra, [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC], extension, Mars 2021. 1991 Mathematics Subject Classification. 13A18 (12J10 14E15) valuation, Commutative Algebra (math.AC), Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry, famille admise, FOS: Mathematics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], paire minimale, Algebraic Geometry (math.AG), valuation
Abstract

Let $(K, \nu)$ be a valued field, the notions of \emph{augmented valuation}, of \emph{limit augmented valuation} and of \emph{admissible family} of valuations enable to give a description of any valuation $\mu$ of $K [x]$ extending $\nu$. In the case where the field $K$ is algebraically closed, this description is particularly simple and we can reduce it to the notions of \emph{minimal pair} and \emph{pseudo-convergent family}. Let $(K, \nu )$ be a henselian valued field and $\bar\nu$ the unique extension of $\nu$ to the algebraic closure $\bar K$ of $K$ and let $\mu$ be a valuation of $ K [x]$ extending $\nu$, we study the extensions $\bar\mu$ from $\mu$ to $\bar K [x]$ and we give a description of the valuations $\bar\mu_i$ of $\bar K [x]$ which are the extensions of the valuations $\mu_i$ belonging to the admissible family associated with $\mu$., Comment: in French

Published
2020

3. Irreducibility criterion for quasi-ordinary polynomials

Author

Abdallah Assi, Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS), and Univ Angers, Okina

Subjects
Polynomial, Root of unity, MathematicsofComputing_NUMERICALANALYSIS, Newton polygon, [MATH] Mathematics [math], Computer Science::Computational Geometry, 32S25, 32S70, Commutative Algebra (math.AC), 01 natural sciences, Combinatorics, Mathematics - Algebraic Geometry, TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, 0103 physical sciences, FOS: Mathematics, 0101 mathematics, Algebraically closed field, [MATH]Mathematics [math], Algebraic Geometry (math.AG), Mathematics, Formal power series, Semigroup, Applied Mathematics, 010102 general mathematics, Mathematics - Commutative Algebra, Properties of polynomial roots, Discriminant, 010307 mathematical physics, Geometry and Topology
Abstract

We give a criterion for a quasi-ordinary polynomial to be irreducible. The criterion is based on the notion of approximate roots and that of generalized Newton polygons., 12 pages

Published
2012

4. Lemme d'Artin–Rees, théorème d'Izumi et fonction de Artin

Author

Guillaume Rond, Institut de Mathématiques de Marseille (I2M), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), and Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Pure mathematics, Polynomial, [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC], Commutative Algebra (math.AC), 01 natural sciences, Mathematics - Algebraic Geometry, Fonction de Artin, Mathematics::Group Theory, 0103 physical sciences, Artin L-function, FOS: Mathematics, Théorème d'approximation forte de Artin, 0101 mathematics, Algebraic Geometry (math.AG), ComputingMilieux_MISCELLANEOUS, Mathematics, Discrete mathematics, Lemma (mathematics), Algebra and Number Theory, Mathematics::Commutative Algebra, 010102 general mathematics, Mathematics::Rings and Algebras, Théorème d'Izumi, Clôture intégrale d'idéaux, Artin's conjecture on primitive roots, Mathematics - Commutative Algebra, 16. Peace & justice, Lemme d'Artin–Rees, Conductor, Artin approximation theorem, Bounded function, 010307 mathematical physics, Artin reciprocity law
Abstract

We interpret the Artin-Rees lemma and the Izumi theorem in term of Artin function and we obtain a stable version of the Artin-Rees lemma. We present different applications of these interpretations. First we show that the Artin function of $X_1X_2-X_3X_4$, as a polynomial in the ring of power series in more than three variables, is not bounded by an affine function. Then we prove that the Artin functions of a class of polynomials are bounded by affine functions and we use this to compute approximated integral closures of ideals., Comment: to appear in J. of Algebra; a lot of misprints changed and some proofs are improved following referee's comments

Published
2006

5. Rang maximal pour $T_P^n$

Author

Francois Lauze

Subjects
Discrete mathematics, General Mathematics, Algebraic geometry, Rank (differential topology), Commutative Algebra (math.AC), Mathematics - Commutative Algebra, 13D02 (primary) 14F99 14M99 14N99, Mathematics - Algebraic Geometry, Number theory, FOS: Mathematics, Projective space, Tangent vector, Ideal (ring theory), Algebraically closed field, Algebraic Geometry (math.AG), General position, Mathematics
Abstract

In this paper, I compute the last non-trivial term of the minimal free resolution of the homogeneous ideal of $s$ points of $P^n$ in sufficiently general position, for any $s$, showing that this term is the one conjectured by the Minimal Resolution Conjecture of Anna Lorenzini. I use a geometrical method, the "vectorial m\'ethode d'Horace" developped by Andr\'e Hirschowitz and Carlos Simpson to get a proof of the MRC for $s$ large enough., Comment: LateX 2e, in french, no more accents, major revision

Published
1995

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