On a spectral sequence for equivariant K-theory |
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Authors: | Marc Levine and Christian Serpé |
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Institution: | (1) Department of Mathematics, Northeastern University, Boston, MA 02115, USA;(2) Mathematisches Institut, Fachbereich Mathematik und Informatik, Universit?t Münster, Einsteinstrasse 62, 48149 Münster, Germany |
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Abstract: | We apply the “homotopy coniveau” 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.
The first-named author gratefully acknowledges the support of the Humboldt Foundation through the Wolfgang Paul Program, and
support of the NSF via grants DMS-0140445 and DMS-0457195. |
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Keywords: | Algebraic cycles Equivariant K-theory Atiyah– Hirzebruch spectral sequence Higher Chow groups |
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