Fibrewise stratification of group representations

Dave Benson; Srikanth B. Iyengar; Henning Krause; Julia Pevtsova

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arXiv · 2204.10431

Fibrewise stratification of group representations

Dave Benson·Srikanth B. Iyengar·Henning Krause·Julia Pevtsova

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Abstract

Given a finite cocommutative Hopf algebra $A$ over a commutative regular ring $R$, the lattice of localising tensor ideals of the stable category of Gorenstein projective $A$-modules is described in terms of the corresponding lattices for the fibres of $A$ over the spectrum of $R$. Under certain natural conditions on the cohomology of $A$ over $R$, this yields a stratification of the stable category. These results apply when $A$ is the group algebra over $R$ of a finite group, and also when $A$ is the exterior algebra on a finite free $R$-module.

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BibTeX RIS

Dave Benson, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova. 2022-04-21. Fibrewise stratification of group representations. https://arxiv.org/abs/2204.10431

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