The Singularity Category Of An Exact Category Applied To Characterize Gorenstein Schemes. (13th June 2022)

• Record Type: Journal Article
• Authors: Christensen, Lars Winther; Ding, Nanqing; Estrada, Sergio; Hu, Jiangsheng; Li, Huanhuan; Thompson, Peder
• Is Part Of: Quarterly journal of mathematics. Volume 74:Part 1(2023)
• Page Start: 1
• Page End: 27
• Publication Date: 2022-06-13
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/qmath/haac013
• Languages: English
• ISSNs: 0033-5606

Abstract

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.