The Singularity Category Of An Exact Category Applied To Characterize Gorenstein Schemes
Date
2023
Authors
Christensen, Lars Winther (TTU)
Ding, Nanqing
Estrada, Sergio
Hu, Jiangsheng
Li, Huanhuan
Thompson, Peder
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We construct a non-affine analogue of the singularity category of a Gorenstein local ring. With this, Buchweitz’s classic equivalence of three triangulated categories over a Gorenstein local ring has been generalized to schemes, a project started by Murfet and Salarian more than ten years ago. Our construction originates in a framework we develop for singularity categories of exact categories. As an application of this framework in the non-commutative setting, we characterize rings of finite finitistic dimension.
Description
This is a pre-copyedited, author-produced version of an article accepted for publication in The Quarterly Journal of Mathematics following peer review. The version of record is available online at: https://doi.org/10.1093/qmath/haac013.
Rights
Availability
Keywords
Cotorsion Pair, Defect Category, Finitistic Dimension, Global Dimension, Gorenstein Scheme, Singularity Category
Citation
Christensen, L. W., Ding, N., Estrada, S., Hu, J., Li, H., & Thompson, P. (2022). The Singularity Category Of An Exact Category Applied To Characterize Gorenstein Schemes. Quarterly Journal of Mathematics, 74(1), 1–27. https://doi.org/10.1093/qmath/haac013