The Nakayama functor and its completion for Gorenstein algebras

DOI10.24033/bsmf.2849zbMath1505.16020arXiv2010.05676OpenAlexW3092572217MaRDI QIDQ5869834

Srikanth B. Iyengar, Henning Krause

Publication date: 29 September 2022

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.05676

zbMATH Keywords

Gorenstein algebraSerre dualityNakayama functorlocal dualityGorenstein-projective modulestable module category

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Local cohomology and commutative rings (13D45) Module categories and commutative rings (13C60) Stable module categories (18G65)

Related Items

Virtually Gorenstein rings and relative homology of complexes

Cites Work

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• Vanishing of \(Ext^ i_ R(M,R)\)
• Finite Hochschild cohomology without finite global dimension.
• Duality in algebra and topology
• Singularity categories, Schur functors and triangular matrix rings
• The Auslander-Reiten formula for complexes of modules.
• The homotopy category of flat modules, and Grothendieck duality
• On rings with self-injective dimension \(\leq 1\)
• The homotopy category of complexes of projective modules
• Gorenstein injective and projective modules
• Support varieties and modules of finite projective dimension for modular Lie superalgebras
• A generalization of the Nakayama functor
• Support and injective resolutions of complexes over commutative rings
• Stable cohomology over local rings
• Acyclicity versus total acyclicity for complexes over noetherian rings
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Injective dimension of semi-primary rings
• On the ubiquity of Gorenstein rings
• Towards a theory of Bass numbers with application to Gorenstein algebras
• Support theory via actions of tensor triangulated categories
• Residues and duality for singularity categories of isolated Gorenstein singularities
• Stratifying triangulated categories
• Maximal Cohen–Macaulay Modules and Tate Cohomology
• REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS
• LOCAL DUALITY FOR THE SINGULARITY CATEGORY OF A FINITE DIMENSIONAL GORENSTEIN ALGEBRA
• Local duality for representations of finite group schemes
• The connection between the $K$-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
• Des catégories abéliennes
• the stable derived category of a noetherian scheme
• Homological and homotopical aspects of torsion theories