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Fibrewise stratification of group representations
- Publication Year :
- 2022
-
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.<br />Comment: 26 pages. Clarified connections to the work of Lau (arXiv:2101.01446). The introduction has been rewritten a little
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2204.10431
- Document Type :
- Working Paper