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Representations of finite groups on modules over K-theory (with an appendix by Akhil Mathew)

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arxiv 1503.02477 v1 pith:EHNL3MUE submitted 2015-03-09 math.RT math.AT

David Treumann This is my paper · ORCID
classification math.RTmath.AT
keywords mathbffinitemodulesrepresentationsringspectrumtheoryactions
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abstract

Let $G$ be a finite group, and let $\mathbf{K}_p$ denote the completion at $p$ of the complex $K$-theory spectrum. $\mathbf{K}_p$ is a commutative ring spectrum that in some ways is very similar to the usual ring $\mathbf{Z}_p$ of $p$-adic integers. We discuss $G$-actions on $\mathbf{K}_p$-modules, and propose to study them by analogy with the classical theory of modular representations of $G$.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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.

  2. Geometrization of summation formulae for quadrics

    math.NT 2026-05 unverdicted novelty 6.0 of 10

    Geometrizes Poisson summation for quadrics over number fields by relating Braverman-Kazhdan and theta-lift Schwartz spaces.

  3. Weyl algebras on Braverman-Kazhdan spaces

    math.RT 2026-05 unverdicted novelty 4.0 of 10

    Studies differential operators on Braverman-Kazhdan spaces P^der backslash G and claims they share structural properties with Weyl algebras while developing D-module theory.

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