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A general Greenlees-May splitting principle

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arxiv 2405.18885 v1 pith:RS4K5DRN submitted 2024-05-29 math.KT math.ATmath.OA

Serge Bouc , Ivo Dell'Ambrogio , Rubén Martos This is my paper · ORCID
classification math.KTmath.ATmath.OA
keywords algebraiccategoryequivariantfunctorgreenmackeyalgebrasarbitrary
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abstract

In equivariant topology, Greenlees and May used Mackey functors to show that, rationally, the stable homotopy category of $G$-spectra over a finite group $G$ splits as a product of simpler module categories. We extend the algebraic part (also independently proved by Th\'evenaz and Webb) of this classical result to Mackey modules over an arbitrary Green functor, and use the case of the complex representation ring Green functor to obtain an algebraic model of the rational equivariant Kasparov category of $G$-cell algebras.

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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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