Comparisons between singularity categories and relative stable categories of finite groups

Baland, S. and Stevenson, G. (2019) Comparisons between singularity categories and relative stable categories of finite groups. Journal of Pure and Applied Algebra, 223(3), pp. 948-964. (doi:10.1016/j.jpaa.2018.05.008)

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Abstract

We consider the relationship between the relative stable category of and the usual singularity category for group algebras with coefficients in a commutative noetherian ring. When the coefficient ring is self-injective we show that these categories share a common, relatively large, Verdier quotient. At the other extreme, when the coefficient ring has finite global dimension, there is a semi-orthogonal decomposition, due to Poulton, relating the two categories. We prove that this decomposition is partially compatible with the monoidal structure and study the morphism it induces on spectra.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Stevenson, Dr Gregory
Authors: Baland, S., and Stevenson, G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Pure and Applied Algebra
Publisher:Elsevier
ISSN:0022-4049
ISSN (Online):1873-1376
Published Online:24 May 2018

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