Algebraic Cycles and Completions of Equivariant K-theory
نویسندگان
چکیده
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 5.5) which gives a description of the completion of the equivariant Grothendieck group G0(G,X)⊗ C at any maximal ideal of the representation ring R(G) ⊗ 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.
منابع مشابه
1 5 Ju n 20 09 COMPLETIONS OF HIGHER EQUIVARIANT K - THEORY
For a linear algebraic group G acting on a smooth variety X over an algebraically closed field k of characteristic zero, we prove a version of nonabelian localization theorem for the rational higher equivariant K-theory of X . This is then used to establish a Riemann-Roch theorem for the completion of the rational higher equivariant K-theory at a maximal ideal of the representation ring of G.
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