Stratifying integral representations via equivariant homotopy theory

Tobias Barthel

Stratifying integral representations via equivariant homotopy theory

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arxiv 2203.14946 v1 pith:SHO3SDBT submitted 2022-03-28 math.AT math.RT

Tobias Barthel This is my paper · ORCID

classification math.ATmath.RT

keywords representationslinearapplicationcategoryclassificationcommutativederivedequivariant

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abstract

We prove that the derived category of $R$-linear representations of a finite group $G$ is stratified for any regular commutative ring $R$. As an application, we obtain a classification of localizing tensor ideals of ordinary $R$-linear $G$-representations whose underlying $R$-module is projective.

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Convexity in tensor triangular geometry
math.CT 2025-06 accept novelty 7.0 of 10

In locally cohomologically stratified tensor triangular categories with noetherian spectrum, the dualizable localizing ideals are exactly the localizing ideals supported on convex subsets of the Balmer spectrum.

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