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).