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

2015/03/09 by David Treumann, Treumann, David · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1503.02477

openalex publication_date 2015/03/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Zur Darstellungstheorie der Gruppen endlicher Ordnung. II

Cited by

• Stratifying integral representations of finite groups

Related

• The Module Structure of a Group Action on a Ring
• Equivariant algebraic K-theory of G-rings
• Module schemes in invariant theory
• K-theory as an Eilenberg-Maclane spectrum
• Properties of Breuil-Kisin modules inherited by p-divisible groups