On a spectral sequence for equivariant K-theory

Abstract

We apply the machinery developed by the first-named author to the K-theory of coherent G-sheaves on a finite type G-scheme X over a field, where G is a finite group. This leads to a definition of G-equivariant higher Chow groups (different from the Chow groups of classifying spaces constructed by Totaro and generalized to arbitrary X by Edidin-Graham) and an Atiyah-Hirzebruch spectral sequence from the G-equivariant higher Chow groups to the higher K-theory of coherent G-sheaves on X. This spectral sequence generalizes the spectral sequence from motivic cohomology to K-theory constructed by Bloch-Lichtenbaum and Friedlander-Suslin.

25 pages. The 1st version omitted the bibliography, included in the 2nd version. This 3rd version corrects some references and attributions in the abstract and introduction

Cited by in corpus (1)

• Bordisms of manifolds with proper action of a discrete group: signatures and descriptions of $G$-bundles