Voevodsky motives of stacks of coherent sheaves on a curve

TL;DR

This paper derives formulas for the motives of stacks of coherent sheaves on a smooth projective curve within Voevodsky's mixed motives category, advancing the understanding of their motivic structure.

Contribution

It provides explicit formulas for the motives of stacks of coherent sheaves of fixed rank and degree, a novel result in the context of Voevodsky's motives.

Findings

Formulas for motives of stacks of coherent sheaves on a curve

Application of Voevodsky's triangulated category of mixed motives

Enhanced understanding of the motivic structure of moduli stacks

Abstract

We prove formulae for the motives of stacks of coherent sheaves of fixed rank and degree over a smooth projective curve in Voevodsky's triangulated category of mixed motives with rational coefficients.