The Nakayama functor and its completion for Gorenstein algebras
Rings and Algebras
2022-01-21 v2 Commutative Algebra
Abstract
Duality properties are studied for a Gorenstein algebra that is finite and projective over its center. Using the homotopy category of injective modules, it is proved that there is a local duality theorem for the subcategory of acyclic complexes of such an algebra, akin to the local duality theorems of Grothendieck and Serre in the context of commutative algebra and algebraic geometry. A key ingredient is the Nakayama functor on the bounded derived category of a Gorenstein algebra, and its extension to the full homotopy category of injective modules.
Keywords
Cite
@article{arxiv.2010.05676,
title = {The Nakayama functor and its completion for Gorenstein algebras},
author = {Srikanth B. Iyengar and Henning Krause},
journal= {arXiv preprint arXiv:2010.05676},
year = {2022}
}
Comments
36 pages; there are significant changes from first version. This manuscript will appear in the Bulletin Soc. Math. France