Fibrewise stratification of group representations. (English) Zbl 07888042
Summary: 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.
MSC:
| 16G30 | Representations of orders, lattices, algebras over commutative rings |
| 18G80 | Derived categories, triangulated categories |
| 20C10 | Integral representations of finite groups |
| 20J06 | Cohomology of groups |
Keywords:
cocommutative Hopf algebra; group algebra; integral representation; stratification; stable module categoryReferences:
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