Local duality for the singularity category of a finite dimensional Gorenstein algebra

Dave Benson*, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the p-local and p-torsion subcategories of the derived category, for each homogeneous prime ideal p arising from the action of a commutative ring via Hochschild cohomology.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalNagoya Mathematical Journal
Volume244
Early online date25 Feb 2021
DOIs
Publication statusPublished - 1 Dec 2021

Bibliographical note

Acknowledgments. We are grateful to the American Institute of Mathematics in San Jose, California for supporting this project by their “Research in Squares” program. Our thanks also to a referee for reading this document with care and offering constructive criticism.
The second author was partly supported by the National Science Foundation grants DMS-1503044 and DMS-1700985. The fourth author was partly supported by the National Science Foundation grants DMS-1501146 and DMS-1901854.

Keywords

  • SUPPORT VARIETIES
  • COHOMOLOGY

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