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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