On a spectral sequence for equivariant K-theory

Marc Levine; Christian Serpé

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On a spectral sequence for equivariant K-theory

Marc Levine·Christian Serpé

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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.

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Marc Levine, Christian Serpé. 2005-11-19. On a spectral sequence for equivariant K-theory. https://arxiv.org/abs/math/0511394

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