Bonn Topology Group - Abstracts

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Talk

April 29, 2026
Kaif Hilman (MPI Bonn): Equivariant localising motives for finite groups and applications

Abstract

In this talk, I will give a proposal for a definition of genuine equivariant localising motives for finite groups G. Using isotropy separation arguments on equivariant cubes and the recent insights of Ramzi-Sosnilo-Winges, we use this version of motives to enhance the algebraic K-theory functor with the structure of multiplicative norms. Among other things, we use our results to give a new and much simplified proof that K-theory admits polynomial functoriality, first proved in a celebrated paper of Barwick-Glasman-Mathew-Nikolaus. Time permitting, we will also discuss other applications such as constructing an equivariant Dennis trace map and showing that all genuine G-spectra are the K-theory of a G-stable category. This reports on joint work with Maxime Ramzi.

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