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.

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