Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Wednesday, 20 June 2007, 11:00-12:00, room 401.

Professor Shun-ichi Kimura (Hiroshima University): Bloch's conjecture and Weil conjecture - an introduction to finite dimensionality of motives.

Abstract:

Bloch's conjecture predicts that if X is a surface over C with q(X)=p_g(X)=0, then its infinite symmetric product is rationally connected. It is a brave conjecture, because if X is of general type, then its finite symmetric product SⁿX is also of general type, hence cannot be covered by rational curves. There exist surfaces of general type with q(X)=p_g(X)=0. In this talk, we give a reason why we can believe Bloch's conjecture, from the viewpoint of motives.