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29 March 2024
 
  » arxiv » math.AG/9905081

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Riemann-Roch for equivariant Chow groups
Dan Edidin ; William Graham ;
Date 13 May 1999
Subject Algebraic Geometry; K-Theory and Homology | math.AG math.KT
AbstractThe 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.
Source arXiv, math.AG/9905081
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