(HoRSe seminar) Motivic sheaves over excellent schemes

(HoRSe seminar) Motivic sheaves over excellent schemes

Tue, 01/06/2010
14:00 		Denis-Charles Cisinski (Paris 13) Algebraic and Symplectic Geometry Seminar Add to calendar L2
(HoRSe seminar) Motivic sheaves over excellent schemes
Starting from Morel and Voevodsky's stable homotopy theory of schemes, one defines, for each noetherian scheme of finite dimension $ X $, the triangulated category $ DM(X) $ of motives over $ X $ (with rational coefficients). These categories satisfy all the the expected functorialities (Grothendieck's six operations), from which one deduces that $ DM $ also satisfies cohomological proper descent. Together with Gabber's weak local uniformisation theorem, this allows to prove other expected properties (e.g. finiteness theorems, duality theorems), at least for motivic sheaves over excellent schemes.