The tt-geometry of permutation modules. Part I: Stratification
Paul Balmer, Martin Gallauer
TL;DR
This paper studies the structure of permutation modules over finite groups in positive characteristic, using stratification techniques to analyze their derived categories and tt-spectrum, with various examples illustrating the concepts.
Contribution
It introduces a stratification of the derived category of permutation modules via Brauer quotients and describes the tt-spectrum of compact objects, advancing understanding of their tensor triangulated structure.
Findings
Stratification of the derived category using Brauer quotients
Description of the tt-spectrum of compact objects
Examples illustrating the stratification and spectrum
Abstract
We consider the derived category of permutation modules over a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the set underlying the tt-spectrum of compact objects, and discuss several examples.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry