Higher algebraic K-theory of group actions with finite stabilizers

Details Higher algebraic K-theory of group actions with finite stabilizers Higher algebraic K-theory of group actions with finite stabilizers

1999-12-19

arxiv.org/abs/math/9912155v2

Mathematics

Algebraic Geometry

39 pages, no figures, ScientificWord 2.0. Final revised version accepted for publication in Duke Math. J

Scientific paper

We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over a field on regular separated noetherian algebraic spaces, under the hypothesis that the actions have finite geometric stabilizers and satisfy a rationality condition together with a technical condition which holds e.g. for G abelian or smooth. We describe in an Appendix various complicial bi-Waldhausen categories (in Thomason's terminology) modelling the equivariant K-theory of regular noetherian separated algebraic spaces.

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