Motivic decomposition of abelian schemes without the Fourier transform

by Prof. Bruno Kahn (University of Paris-6, France)

Tuesday 27 Jul 2010, 11:30 → 12:30 Asia/Kolkata

Maths. Seminar Room A369 (Colaba Campus)

Let $f:A\to S$ be abelian scheme. We rpove that for any $n$ invertible on $S$, the Leray spectral sequence for $f$ with coefficients $Z/n$ degenerates canonically. This is also true for $l$-adic cohomology and for Betti cohomology with integral coefficients if $S$ is a $C$-scheme. We deduce from this some integrality results for the K\"unneth projectors associated to the motive of $A$. This is a joint work with A. Skorobogatov.