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 language | English |
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Pages (from-to) | 1-24 |
Number of pages | 24 |
Journal | Nagoya Mathematical Journal |
Volume | 244 |
Early online date | 25 Feb 2021 |
DOIs | |
Publication status | Published - 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