Riemann-Roch for equivariant Chow groups

DOI10.1215/S0012-7094-00-10239-6zbMath0997.14002arXivmath/9905081OpenAlexW2169209978MaRDI QIDQ1567178

Dan Edidin, William A. Graham

Publication date: 12 November 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9905081

zbMATH Keywords

equivariant \(K\)-theoryequivariant Chow groupequivariant Grothendieck groupequivariant Riemann-Roch theorem

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Riemann-Roch theorems (14C40) Equivariant (K)-theory (19L47)

Related Items (25)

The completion problem for equivariant \(K\)-theory ⋮ Equivariant noncommutative motives ⋮ Equivariant characteristic classes of external and symmetric products of varieties ⋮ Positivity and Kleiman transversality in equivariant \(K\)-theory of homogeneous spaces ⋮ Uniform \(K\)-stability, Duistermaat-Heckman measures and singularities of pairs ⋮ Atiyah-Segal theorem for Deligne-Mumford stacks and applications ⋮ Quantum \(K\)-theory of Grassmannians ⋮ Virtual Coulomb branch and vertex functions ⋮ Virtual Riemann-Roch theorems for almost perfect obstruction theories ⋮ Modified Futaki invariant and equivariant Riemann-Roch formula ⋮ Elliptic genus of singular algebraic varieties and quotients ⋮ Galois structure of homogeneous coordinate rings ⋮ On finite generation of the section ring of the determinant of cohomology line bundle ⋮ Localized operations on \(T\)-equivariant oriented cohomology of projective homogeneous varieties ⋮ Algebraic cycles and completions of equivariant \(K\)-theory ⋮ Riemann-Roch for equivariant \(K\)-theory ⋮ On a spectral sequence for equivariant \(K\)-theory ⋮ Logarithmic trace and orbifold products ⋮ Riemann-Roch for Quotients and Todd Classes of Simplicial Toric Varieties ⋮ Equivariant Grothendieck-Riemann-Roch and localization in operational \(K\)-theory. With an appendix by Gabriele Vezzosi. ⋮ Elliptic genus of phases of \(N=2\) theories ⋮ K-theoretic Hall algebras, quantum groups and super quantum groups ⋮ Virtual equivariant Grothendieck-Riemann-Roch formula ⋮ Higher algebraic \(K\)-theory of group actions with finite stabilizers ⋮ Nonabelian localization in equivariant \(K\)-theory and Riemann --- Roch for quotients

Cites Work

• Intersection theory on algebraic stacks and Q-varieties
• 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
• Riemann-Roch for singular varieties
• Equivariant Chow groups for torus actions
• Equivariant intersection theory (With an appendix by Angelo Vistoli: The Chow ring of \({\mathcal M}_2\))
• Riemann-Roch theorems for Deligne-Mumford stacks
• Comparison of equivariant algebraic and topological K-theory
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
• Groupes de Grothendieck des schemas en groupes reductifs deployes
• The representation ring of a compact Lie group
• Equivariant \(K\)-theory and completion
• Algebraic spaces
• Quotient spaces modulo reductive algebraic groups
• B‐bounded nonlinear semigroups
• Geometric Invariant Theory
• Characteristic classes in the Chow ring
• The Grothendieck-Riemann-Roch theorem for group scheme actions
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