Duke Mathematical Journal

Algebraic cycles and completions of equivariant K-theory

Dan Edidin and William Graham

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Abstract

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

Article information

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

Dates
First available in Project Euclid: 15 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1218811402

Digital Object Identifier
doi:10.1215/00127094-2008-042

Mathematical Reviews number (MathSciNet)
MR2444304

Zentralblatt MATH identifier
1148.14007

Subjects
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]

Citation

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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