The singularity category of an exact category applied to characterize Gorenstein schemes
K-Theory and Homology
2022-05-06 v2 Commutative Algebra
Rings and Algebras
Abstract
We study singularity categories of exact categories with a focus on those associated to a complete hereditary cotorsion pair. As an application we identify a non-affine analogue of the singularity category of a Gorenstein local ring; with this Buchweitz's classic equivalence of three categories over Gorenstein local rings has been generalized to schemes, a project started by Murfet and Salarian more than ten years ago. As another application we use the framework to characterize rings of finite finitistic dimension.
Keywords
Cite
@article{arxiv.2009.03270,
title = {The singularity category of an exact category applied to characterize Gorenstein schemes},
author = {Lars Winther Christensen and Nanqing Ding and Sergio Estrada and Jiangsheng Hu and Huanhuan Li and Peder Thompson},
journal= {arXiv preprint arXiv:2009.03270},
year = {2022}
}
Comments
Minor revisions. Final version, to appear in Q.J. Math; 24 pp