The derived ∞-category of permutation modules is equivalent to modules over the Eilenberg-MacLane spectrum of the constant Mackey functor, and the equivariant modular fixed point functor recovers Balmer-Gallauer's, giving a new proof of Miller's Picard group classification for p-groups.
The tt-geometry of permutation modules. Part I: Stratification
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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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Modular fixed points in equivariant homotopy theory
The derived ∞-category of permutation modules is equivalent to modules over the Eilenberg-MacLane spectrum of the constant Mackey functor, and the equivariant modular fixed point functor recovers Balmer-Gallauer's, giving a new proof of Miller's Picard group classification for p-groups.