The Singularity Category Of An Exact Category Applied To Characterize Gorenstein Schemes-Reference-Cited by-同舟云学术

The Singularity Category Of An Exact Category Applied To Characterize Gorenstein Schemes

Published:2022-06-13 Issue:1 Volume:74 Page:1-27
ISSN:0033-5606
Container-title:The Quarterly Journal of Mathematics
language:en
Short-container-title:

Author:

Christensen Lars Winther¹,Ding Nanqing²,Estrada Sergio³,Hu Jiangsheng⁴,Li Huanhuan⁵,Thompson Peder⁶⁷

Affiliation:

1. Department of Mathematics and Statistics, Texas Tech University , Lubbock, TX 79409, USA

2. Department of Mathematics, Nanjing University , Nanjing 210093, China

3. Departamento de Matemáticas, Universidad de Murcia , Murcia 30100, Spain

4. School of Mathematics and Physics, Jiangsu University of Technology , Changzhou 213001, China

5. School of Mathematics and Statistics, Xidian University , Xi’an 710071, China

6. Mathematics Department Norwegian University of Science and Technology , 7491 Trondheim, Norway

7. Niagara University, Niagara University , NY 14109, USA

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.

Funder

Simons Foundation

National Natural Science Foundation

Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/qjmath/article-pdf/74/1/1/49946674/haac013.pdf

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