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

DOI10.1016/j.aim.2005.06.010zbMath1093.19004arXivmath/0411213OpenAlexW2088349898MaRDI QIDQ2577007

Dan Edidin, William A. Graham

Publication date: 29 December 2005

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411213

zbMATH Keywords

equivariant \(K\)-theoryRiemann-Roch theorems

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) (K)-theory of schemes (19E08) Generalizations (algebraic spaces, stacks) (14A20) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items (15)

Cominuscule points and Schubert varieties ⋮ Inertial Chow rings of toric stacks ⋮ Counting sheaves on Calabi-Yau 4-folds. I ⋮ Atiyah-Segal theorem for Deligne-Mumford stacks and applications ⋮ Shadows of characteristic cycles, Verma modules, and positivity of Chern-Schwartz-MacPherson classes of Schubert cells ⋮ Virtual pullbacks in K-theory ⋮ Galois structure of homogeneous coordinate rings ⋮ Localizing virtual structure sheaves for almost perfect obstruction theories ⋮ Stringy K-theory and the Chern character ⋮ Algebraic cycles and completions of equivariant \(K\)-theory ⋮ Riemann-Roch for equivariant \(K\)-theory ⋮ Logarithmic trace and orbifold products ⋮ Adams operations on the virtual K-theory of ℙ(1,n) ⋮ Virtual equivariant Grothendieck-Riemann-Roch formula ⋮ Orbifold products for higher \(K\)-theory and motivic cohomology

Cites Work

• Quotients by groupoids
• Lefschetz-Riemann-Roch theorem and coherent trace formula
• Equivariant algebraic vs. topological K-homology Atiyah-Segal-style
• A Lefschetz formula in equivariant algebraic \(K\)-theory
• Elliptic operators and compact groups
• Riemann-Roch for singular varieties
• Equivariant intersection theory (With an appendix by Angelo Vistoli: The Chow ring of \({\mathcal M}_2\))
• Riemann-Roch for equivariant Chow groups
• Riemann-Roch theorems for Deligne-Mumford stacks
• Comparison of equivariant algebraic and topological K-theory
• Higher algebraic \(K\)-theory of group actions with finite stabilizers
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Première partie). Rédigé avec la colloboration de J. Dieudonné
• Equivariant K-theory
• The representation ring of a compact Lie group
• Algebraic spaces
• Higher algebraic K-theory: I
• Diagonalizably linearized coherent sheaves
• Geometric Invariant Theory
• Riemann-Roch for Quotients and Todd Classes of Simplicial Toric Varieties
• Algebraic \(K\)-theory.
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