## Title

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

## Speaker

Dr. Simon Pepin Lehalleur

## Abstract

I will recall basic features of Voevodsky's category of mixed motives

and explain how to define the motives of certain algebraic stacks in

this context. I will then state and sketch the proof of a formula for the

motive with rational coefficients of the stack of vector bundles over

a smooth projective curve. This formula is compatible with classical

computations of various cohomological invariants of this stack by

Harder, Atiyah-Bott, Behrend-Dhillon, etc. The proof uses

rigidifications of the stack by certain Quot and Flag-Quot schemes as

well as a motivic version of an argument of Laumon and Heinloth on the

relative cohomology of small maps. This is joint work with Victoria

Hoskins (FU Berlin).

### Time & Location

Nov 01, 2018 | 02:00 PM c.t. - 04:00 PM

A6/SR 007/008