Nonabelian localization in equivariant K-theory and Riemann-Roch for quotients

被引：18

作者：

Edidin, D ^{[1
]}

Graham, W

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Univ Georgia, Dept Math, Boyd Grad Studies Res Ctr, Athens, GA 30602 USA

来源：

ADVANCES IN MATHEMATICS | 2005年 / 198卷 / 02期

关键词：

equivariant K-theory; Riemann-Roch theorems;

D O I：

10.1016/j.aim.2005.06.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a localization formula in equivariant algebraic K-theory for an arbitrary complex algebraic group acting with finite stabilizer on a smooth algebraic space. This extends to non-diagonalizable groups the localization formulas of Nielsen [Diagonalizably linearized coherent sheaves, Bull. Soc. Math. France 102 (1974) 85-97] and Thomason [Une formule de Lefschetz en K-theorie equivariante algebrique, Duke Math. J. 68(3) (1992) 447-462]. As an application we give a Riemann-Roch formula for quotients of smooth algebraic spaces by proper group actions. This formula extends previous work of Toen [Theoremes de Riemann-Roch pour les champs de Deligne-Mumford, K-Theory 18(1) (1999) 33-76] and the authors [Riemann-Roch for quotients and Todd classes of sirnplicial toric varieties, Comm. Algebra 31 (2003) 3735-3752]. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：547 / 582

页数：36

共 30 条

[1] [Anonymous], 1967, I HAUTES ETUDES SCI
[2] Atiyah M., 1974, LECT NOTES MATH, V401, DOI 10.1007/BFb0057821
[3] BAUM P, 1975, I HAUTES ETUDES SCI, V45
[4] BOREL A, 1991, LINEAR ALGEBRAIC GRO
[5] Brocker T., 1995, GRADUATE TEXTS MATH, V98
[6] Chriss N., 1997, Representation Theory and Complex Geometry
[7] Edidin D, 2000, DUKE MATH J, V102, P567
[8] Riemann-Roch for quotients and Todd classes of simplicial toric varieties
Edidin, D
Graham, W
[J]. COMMUNICATIONS IN ALGEBRA, 2003, 31 (08) : 3735 - 3752
[9] Fulton W., 2013, INTERSECTION THEORY, DOI DOI 10.1007/978-3-662-02421-8
[10] Grothendieck A., 1966, I HAUTES ETUDES SCI, V28

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