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The Singularity Category Of An Exact Category Applied To Characterize Gorenstein Schemes
Department of Mathematics and Statistics, Texas Tech University , Lubbock, TX 79409, USA.
Department of Mathematics, Nanjing University , Nanjing 210093, China.
Departamento de Matemáticas, Universidad de Murcia , Murcia 30100, Spain.
School of Mathematics and Physics, Jiangsu University of Technology , Changzhou 213001, China.
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2023 (English)In: Quarterly Journal of Mathematics, ISSN 0033-5606, E-ISSN 1464-3847, Vol. 74, no 1, p. 1-27Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
2023. Vol. 74, no 1, p. 1-27
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
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URN: urn:nbn:se:mdh:diva-64382DOI: 10.1093/qmath/haac013ISI: 000964291800001Scopus ID: 2-s2.0-85153966626OAI: oai:DiVA.org:mdh-64382DiVA, id: diva2:1801329
Available from: 2023-09-29 Created: 2023-09-29 Last updated: 2024-01-24Bibliographically approved

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Thompson, Peder

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