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

Anderson D.; Gonzales R.; Payne S.; Vezzosi G. · Algebra and Number Theory (2021) · DOI: 10.2140/ant.2021.15.341

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.

Instituciones: Pontificia Universidad Católica del Perú