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Algebraic cycles and completions of equivariant K-theory | | Dan Edidin
; William Graham
; | | Date: |
22 Feb 2007 | | Subject: | Algebraic Geometry; K-Theory and Homology | | Abstract: | Let $G$ be a complex, linear algebraic group acting on an algebraic space $X$. The purpose of this paper is to prove a Riemann-Roch theorem (Theorem 5.3) which gives a description of the completion of the equivariant Grothendieck group $G_0(G,X)$ at any maximal ideal of the representation ring $R(G) otimes C$ in terms of equivariant cycles. The main new technique for proving this theorem is our non-abelian completion theorem (Theorem 4.3) for equivariant $K$-theory. Theorem 4.3 generalizes the classical localization theorems for diagonalizable group actions to arbitrary groups. | | Source: | arXiv, math/0702671 | | Services: | Forum | Review | PDF | Favorites | |
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