Equivariant Chern character for coherent sheaves and Riemann-Roch-Grothendieck

TL;DR

This paper develops an equivariant Chern character theory for coherent sheaves on complex manifolds with group actions and proves a related Riemann-Roch-Grothendieck theorem, extending classical results to an equivariant setting.

Contribution

It introduces an equivariant Chern character theory valued in Bott-Chern cohomology and establishes a corresponding Riemann-Roch-Grothendieck theorem for coherent sheaves.

Findings

Defined equivariant Chern characters in Bott-Chern cohomology

Proved the Riemann-Roch-Grothendieck theorem in the equivariant context

Extended classical theorems to manifolds with finite group actions

Abstract

In this paper, we develope an equivariant theory of Chern characters for coherent sheaves on compact complex manifolds with finite group actions, taking values in Bott-Chern cohomology classes. Furthermore, we establish the corresponding Riemann-Roch-Grothendieck theorem in this context.