A formula for the Voevodsky motive of the moduli stack of vector bundles on a curve

TL;DR

This paper derives a formula for the Voevodsky motive of the moduli stack of vector bundles on a smooth projective curve, advancing the understanding of motives in algebraic geometry.

Contribution

It provides a new explicit formula for the motive of the moduli stack of vector bundles in Voevodsky's category, a significant step in motive computations.

Findings

Derived an explicit formula for the motive of the moduli stack

Enhanced understanding of motives in algebraic geometry

Contributed to the theory of Voevodsky's mixed motives

Abstract

We prove a formula for the motive of the stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's triangulated category of mixed motives with rational coefficients.