Comparisons between singularity categories and relative stable categories of finite groups

Shawn Baland; Greg Stevenson

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arXiv · 1601.07727

Comparisons between singularity categories and relative stable categories of finite groups

Shawn Baland·Greg Stevenson

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Abstract

We consider the relationship between the relative stable category of Benson, Iyengar, and Krause 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.

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BibTeX RIS

Shawn Baland, Greg Stevenson. 2016-02-24. Comparisons between singularity categories and relative stable categories of finite groups. https://arxiv.org/abs/1601.07727

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