Duke Mathematical Journal

Algebraic cycles and completions of equivariant K-theory

Dan Edidin and William Graham

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Let G be a complex, linear algebraic group acting on an algebraic space X. The purpose of this article is to prove a Riemann-Roch theorem (Theorem 6.5) that 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 nonabelian completion theorem (Theorem 5.3) for equivariant K-theory. Theorem 5.3 generalizes the classical localization theorems for diagonalizable group actions to arbitrary groups

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Duke Math. J., Volume 144, Number 3 (2008), 489-524.

First available in Project Euclid: 15 August 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14C40: Riemann-Roch theorems [See also 19E20, 19L10] 19D10: Algebraic $K$-theory of spaces
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]


Edidin, Dan; Graham, William. Algebraic cycles and completions of equivariant $K$ -theory. Duke Math. J. 144 (2008), no. 3, 489--524. doi:10.1215/00127094-2008-042. https://projecteuclid.org/euclid.dmj/1218811402

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