東工大 数論・幾何学セミナー： Simon Pepin Lehalleur 氏

2018年9月5日　講演タイトルとアブストラクトを変更しました。

講演タイトル

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

アブストラクト

　Following Grothendieck's vision that many cohomological invariants of of an algebraic variety should be captured by a common motive, Voevodsky introduced a triangulated category of mixed motives which partially realises this idea. After describing this category, I will 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).