Seminar series
Date
Tue, 01 Jun 2010
Time
14:00 -
15:00
Location
L2
Speaker
Denis-Charles Cisinski
Organisation
Paris 13
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.