Motives of stacks of vector bundles on a curve and applications

Mardi 15 juin 14:00-15:15 - Victoria Hoskins - Université Radboud de Nimègue

Résumé : In joint work with Simon Pepin Lehalleur, we prove a formula for the
motive of the moduli stack of vector bundles on a smooth projective
curve in Voevodsky’s triangulated category of motives with rational
coefficients. After stating some key properties of this category and
explaining how to define the motive of this stack, I will outline our
proof, which involves rigidifying this stack using Flag-Quot schemes
parametrising Hecke modifications as well as a motivic version of an
argument of Laumon and Heinloth on the relative cohomology of small
maps. We then use this result to study the motive of moduli spaces of
semistable Higgs bundles, by using Hitchin’s scaling action together
with variation of stability for moduli stacks of chains.

Lieu : Séminaire en ligne

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