| Speaker: | Victoria Hoskins (Freie Universität Berlin) |
|---|---|
| Title: | A formula for the motive of the moduli stack of vector bundles on a curve |
| Date (JST): | Tue, Sep 18, 2018, 13:15 - 14:45 |
| Place: | Seminar Room A |
| Abstract: | Following Grothendieck's vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some properties of this category, I will explain how to define the motive of certain algebraic stacks. I will then state and sketch a proof for the motive of the moduli stack of vector bundles on a smooth projective curve; this formula is compatible with classical computations of invariants of this stack due to Harder, Atiyah--Bott and Behrend--Dhillon. The proof involves rigidifying this stack using Quot and 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. This is joint work with Simon Pepin Lehalleur. |
| Remarks: | Blackboard talk |
