Riemann-Roch for equivariant Chow groups

Abstract

The purpose of this paper is to prove an equivariant Riemann-Roch theorem for schemes or algebraic spaces with an action of a linear algebraic group $G$. For a $G$-space $X$, this theorem gives an isomorphism between a completion of the equivariant Grothendieck group and a completion of equivariant equivariant Chow groups. The key to proving this isomorphism is a geometric description of completions of the equivariant Grothendieck group. Besides Riemann-Roch, this result has some purely $K$-theoretic applications. In particular, we prove a conjecture of Köck (in the case of regular schemes) and extend to arbitrary characteristic a result of Segal on representation rings.

31 pages, Latex2e. Email for W. Graham is [email protected] Duke Math. Journal, to appear

References in corpus (1)

• Characteristic classes in the Chow ring

Cited by in corpus (1)

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