Virtual equivariant Grothendieck-Riemann-Roch formula

TL;DR

This paper extends the Grothendieck-Riemann-Roch formula to the equivariant setting for schemes with perfect obstruction theories and introduces a virtual non-abelian localization theorem, advancing equivariant algebraic geometry.

Contribution

It generalizes the virtual Grothendieck-Riemann-Roch formula to equivariant schemes and establishes a virtual non-abelian localization theorem.

Findings

Proved a virtual equivariant Grothendieck-Riemann-Roch formula.

Established a virtual non-abelian localization theorem.

Extended previous results to the equivariant context.

Abstract

For a $G$-scheme $X$ with a given equivariant perfect obstruction theory, we prove a virtual equivariant Grothendieck-Riemann-Roch formula, this is an extension of a result of Fantechi-G\"ottsche to the equivariant context. We also prove a virtual non-abelian localization theorem for schemes over $\mathbb{C}$ with proper actions.