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The geometry of permutation modules

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arxiv 2307.04398 v2 pith:6SPZZBGW submitted 2023-07-10 math.RT math.CT

Paul Balmer , Martin Gallauer This is my paper · ORCID
classification math.RTmath.CT
keywords categorymodulespermutationspectrumabelianbrauercharacteristicclassification
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We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the problem to elementary abelian groups and then by using a twisted form of cohomology to express the spectrum locally in terms of the graded endomorphism ring of the unit. Together, these results yield a classification of thick and of localizing ideals.

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  1. The tensor triangular geometry of fully faithful functors

    math.AT 2025-08 accept novelty 8.0 of 10

    Fully faithful tt-functors force their Balmer spectra to be quotients with connected fibers, and the new unitation construction yields explicit equivariant spectrum computations.

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