The forgetful map in rational K-theory
Algebraic Geometry
2007-10-08 v1 K-Theory and Homology
Abstract
Let G be a connected reductive algebraic group acting on a scheme X. Let R(G) denote the representation ring of G, and let I be the ideal in R(G) of virtual representations of rank 0. Let G(X) (resp. G(G,X)) denote the Grothendieck group of coherent sheaves (resp. G-equivariant coherent sheaves) on X. Merkurjev proved that if the fundamental group of G is torsion-free, then the map of G(G,X)/IG(G,X) to G(X) is an isomorphism. Although this map need not be an isomorphism if the fundamental group of G has torsion, we prove that without the assumption on the fundamental group of G, this map is an isomorphism after tensoring with the rational numbers.
Cite
@article{arxiv.0710.1253,
title = {The forgetful map in rational K-theory},
author = {William Graham},
journal= {arXiv preprint arXiv:0710.1253},
year = {2007}
}