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195 results on '"Iyengar, Srikanth B."'

152. Annihilation of Cohomology and Strong Generation of Module Categories.

Author

Iyengar, Srikanth B. and Ryo Takahashi

Subjects
*COHOMOLOGY theory, *NOETHER'S theorem, *FINITE element method, *MODULES (Algebra), *COMMUTATIVE rings
Abstract

The cohomology annihilator of a noetherian ring that is finitely generated as a module over its center is introduced. Results are established linking the existence of nontrivial cohomology annihilators and the existence of strong generators for the category of finitely generated modules. Exploiting this link, results of Popescu and Roczen, and Wang concerning cohomology annihilators of commutative rings, and also results of Aihara and Takahashi, Keller and Van den Bergh, and Rouquier on strong finite generation of the corresponding bounded derived category, are generalized to cover excellent local rings and also rings essentially of finite type over a field. [ABSTRACT FROM AUTHOR]

Published
2016
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169. Relation between two twisted inverse image pseudofunctors in duality theory.

Author

Iyengar, Srikanth B., Lipman, Joseph, and Neeman, Amnon

Subjects
*INVERSE functions, *DUALITY theory (Mathematics), *IMAGE processing, *MATHEMATICAL mappings, *NOETHERIAN rings, *ISOMORPHISM (Mathematics)
Abstract

Grothendieck duality theory assigns to essentially finite-type maps $f$ of noetherian schemes a pseudofunctor $f^{\times }$ right-adjoint to $\mathsf{R}f_{\ast }$, and a pseudofunctor $f^{!}$ agreeing with $f^{\times }$ when $f$ is proper, but equal to the usual inverse image $f^{\ast }$ when $f$ is étale. We define and study a canonical map from the first pseudofunctor to the second. This map behaves well with respect to flat base change, and is taken to an isomorphism by ‘compactly supported’ versions of standard derived functors. Concrete realizations are described, for instance for maps of affine schemes. Applications include proofs of reduction theorems for Hochschild homology and cohomology, and of a remarkable formula for the fundamental class of a flat map of affine schemes. [ABSTRACT FROM AUTHOR]

Published
2015
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170. Detecting flatness over smooth bases

Author

Avramov, Luchezar L. and Iyengar, Srikanth B.

Abstract

Given an essentially finite type morphism of schemes $ f\colon X\to Y$, let $ f^{\{d\}}\colon X^{\{d\}}\to Y$-fold fiber product $ X^{\{d\}}= X\times _{Y}\cdots \times _{Y}X$ $ \pi _i\colon X^{\{d\}}\to X$th canonical projection. When $ Y$ $ \mathcal F$, it is proved that $ \mathcal F$ if (and only if) $ f^{\{d\}}$ $ {\bigotimes _{i=1}^d}\pi _i^*{\mathcal F}$, for some "$. The equivalent statement in commutative algebra is an analog--but not a consequence--of a classical criterion of Auslander and Lichtenbaum for the freeness of finitely generated modules over regular local rings.

Published
2012
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171. Gröbner Degenerations

Author

Varbaro, Matteo, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Polini, Claudia, Raicu, Claudiu, Varbaro, Matteo, Walker, Mark E., Conca, Aldo, editor, Iyengar, Srikanth B., editor, and Singh, Anurag K., editor

Published
2021
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172. Koszul Modules

Author

Raicu, Claudiu, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Polini, Claudia, Raicu, Claudiu, Varbaro, Matteo, Walker, Mark E., Conca, Aldo, editor, Iyengar, Srikanth B., editor, and Singh, Anurag K., editor

Published
2021
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173. Adams Operations in Commutative Algebra

Author

Walker, Mark E., Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Polini, Claudia, Raicu, Claudiu, Varbaro, Matteo, Walker, Mark E., Conca, Aldo, editor, Iyengar, Srikanth B., editor, and Singh, Anurag K., editor

Published
2021
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174. Defining Equations of Blowup Algebras

Author

Polini, Claudia, Morel, Jean-Michel, Editor-in-Chief, Teissier, Bernard, Editor-in-Chief, Baur, Karin, Series Editor, Brion, Michel, Series Editor, De Lellis, Camillo, Series Editor, Figalli, Alessio, Series Editor, Huber, Annette, Series Editor, Khoshnevisan, Davar, Series Editor, Kontoyiannis, Ioannis, Series Editor, Kunoth, Angela, Series Editor, Mézard, Ariane, Series Editor, Podolskij, Mark, Series Editor, Serfaty, Sylvia, Series Editor, Vezzosi, Gabriele, Series Editor, Wienhard, Anna, Series Editor, Polini, Claudia, Raicu, Claudiu, Varbaro, Matteo, Walker, Mark E., Conca, Aldo, editor, Iyengar, Srikanth B., editor, and Singh, Anurag K., editor

Published
2021
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194. Noncommutative motives and their applications

Author

Marcolli, Matilde, Tabuada, Gonçalo, Eisenbud, David, Iyengar, Srikanth B., Singh, Anurag K., Stafford, J. Joby, and Van de Bergh, Michel

Subjects
Mathematics::K-Theory and Homology
Abstract

This survey is based on lectures given by the authors during the program “Noncommutative algebraic geometry and representation theory” at the MSRI in the Spring 2013. It covers the recent work [44, 45, 46, 47, 48, 49, 50] on noncommutative motives and their applications, and is intended for a broad mathematical audience. In Section 1 we recall the main features of Grothendieck’s theory of motives. In Sections 2 and 3 we introduce several categories of noncommutative motives and describe their relation with the classical commutative counterparts. In Section 4 we formulate the noncommutative analogues of Grothendieck’s standard conjectures of type C and D, of Voevodsky’s smash-nilpotence conjecture, and of Kimura-O’Sullivan finite-dimensionality conjecture. Section 5 is devoted to recollections of the (super-)Tannakian formalism. In Section 6 we introduce the noncommutative motivic Galois (super-)groups and their unconditional versions. In Section 7 we explain how the classical theory of (intermediate) Jacobians can be extended to the noncommutative world. Finally, in Section 8 we present some applications to motivic decompositions and to Dubrovin’s conjecture.

Published
2015

195. Congruence modules in higher codimension and zeta lines in Galois cohomology.

Author

Iyengar SB, Khare CB, Manning J, and Urban E

Abstract

This article builds on recent work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main results are a criterion for detecting regularity of local rings in terms of congruence modules, and a more refined version of a result tracking the change of congruence modules under deformation. Number theoretic applications include the construction of canonical lines in certain Galois cohomology groups arising from adjoint motives of Hilbert modular forms., Competing Interests: Competing interests statement:The authors declare no competing interest.

Published
2024
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