Kaif Hilmann (Uni Bonn)

Titel: Equivariant localizing motives for finite groups and applications

Abstract: In this talk, I will give a proposal for a definition of genuine equivariant lozalizing 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.