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.
Real Topological Hochschild Homology of Perfectoid Rings
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abstract
We refine several results of Bhatt-Morrow-Scholze on THH to THR. In particular, we compute THR of perfectoid rings. This will be useful for establishing motivic filtrations on real topological Hochschild and cyclic homology of quasisyntomic rings. We also establish a real refinement of the Hochschild-Kostant-Rosenberg theorem.
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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.