## Algebraic cycles and fibrations

### Summary

Summary: Let $f:X \rightarrow B$ be a projective surjective morphism between quasi-projective varieties. The goal of this paper is the study of the Chow groups of $X$ in terms of the Chow groups of $B$ and of the fibres of $f$. One of the applications concerns quadric bundles. When $X$ and $B$ are smooth projective and when $f$ is a flat quadric fibration, we show that the Chow motive of $X$ is &laquo;built&raquo; from the motives of varieties of dimension less than the dimension of $B$.

### Mathematics Subject Classification

14C15, 14C25, 14C05, 14D99

### Keywords/Phrases

algebraic cycles, Chow groups, quadric bundles, motives, Chow--künneth decomposition