Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory

Dave Anderson, Richard Gonzales, Sam Payne, Gabriele Vezzosi

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

4 Citas (Scopus)

Resumen

We produce a Grothendieck transformation from bivariant operational K-theory to Chow, with a Riemann-Roch formula that generalizes classical Grothendieck-Verdier-Riemann-Roch. We also produce Grothendieck transformations and Riemann-Roch formulas that generalize the classical Adams-Riemann-Roch and equivariant localization theorems. As applications, we exhibit a projective toric variety X whose equivariant K-theory of vector bundles does not surject onto its ordinary K-theory, and describe the operational K-theory of spherical varieties in terms of fixed-point data. In an appendix, Vezzosi studies operational K-theory of derived schemes and constructs a Grothendieck transformation from bivariant algebraic K-theory of relatively perfect complexes to bivariant operational K-theory.

Idioma originalInglés
Páginas (desde-hasta)341-385
Número de páginas45
PublicaciónAlgebra and Number Theory
Volumen15
N.º2
DOI
EstadoPublicada - 2021

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