1999/12/19 by Gabriele Vezzosi, Vezzosi, Gabriele, Angelo Vistoli +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #math.KT #msc:14L30 #msc:19E08
paper · pdf · doi:10.48550/arxiv.math/9912155
39 pages, no figures, ScientificWord 2.0. Final revised version accepted for publication in Duke Math. J
arxiv created 2001/05/22 · arxiv updated 2009/11/30
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.