Chow Rings, Decomposition of the Diagonal and the Topology of Families

Chow Rings, Decomposition of the Diagonal and the Topology of Families - Claire Voisin

Claire Voisin
CNRS, Institut de Mathematiques de Jussieu, Paris
November 1, 2011

Summary: These lectures are devoted to the interplay between cohomology and Chow groups of a complex algebraic variety, and also to the consequences, on the topology of a family of smooth projective varieties, of statements concerning Chow groups of the general fiber. A crucial notion is that of coniveau of the cohomology and its conjectural relation with the shape of Chow groups of small dimension. A common theme will be that of decomposition of the diagonal, which will appear in various contexts.