On a spectral sequence for equivariant K-theory

Details On a spectral sequence for equivariant K-theory On a spectral sequence for equivariant K-theory

2005-11-15

arxiv.org/abs/math/0511394v3

Mathematics

K-Theory and Homology

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

Scientific paper

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.

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