Cdh descent in equivariant homotopy K-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.

17 pages. v4: final version, appeared in Documenta; v3: new title & minor improvements

References in corpus (1)

• Higher Topos Theory

Cited by in corpus (6)

• Motivic and Real Etale Stable Homotopy Theory
• K-theory and G-theory of derived algebraic stacks
• The unit map of the algebraic special linear cobordism spectrum
• Algebraic Cobordism and Étale Cohomology
• A^1-homotopy invariance in spectral algebraic geometry
• The homotopy limit problem and the cellular Picard group of Hermitian $K$-theory