Local duality for the singularity category of a finite dimensional Gorenstein algebra
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 AuslanderReiten triangles for the $\mathfrak{p}$local and $\mathfrak{p}$torsion subcategories of the derived category, for each homogeneous prime ideal $\mathfrak{p}$ arising from the action of a commutative ring via Hochschild cohomology.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.01506
 Bibcode:
 2019arXiv190501506B
 Keywords:

 Mathematics  Representation Theory;
 16G10 (primary);
 16G50;
 16E65;
 16E35
 EPrint:
 19 pages