Cdh descent in equivariant homotopy K-theory

TL;DR

This paper develops geometric models for classifying spaces in G-equivariant motivic homotopy theory, demonstrating that the associated homotopy K-theory spectrum is stable under base change and satisfies cdh descent.

Contribution

It introduces new geometric models for classifying spaces and proves cdh descent for equivariant homotopy K-theory, advancing the understanding of equivariant motivic homotopy theory.

Findings

Homotopy K-theory spectrum is stable under arbitrary base change.

Homotopy K-theory of G-schemes satisfies cdh descent.

Construction of geometric models for classifying spaces in G-equivariant motivic homotopy theory.

Abstract

We construct geometric models for classifying spaces of linear algebraic groups in G-equivariant motivic homotopy theory, where G is a tame group scheme. As a consequence, we show that the equivariant motivic spectrum representing the homotopy K-theory of G-schemes (which we construct as an E-infinity-ring) is stable under arbitrary base change, and we deduce that homotopy K-theory of G-schemes satisfies cdh descent.