Algebraic cycles and fibrations
Doc. Math., J. DMV 18, 1521-1553 (2013)
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 «built» from the motives of varieties of dimension less than the dimension of $B$.
Mathematics Subject Classification
14C15, 14C25, 14C05, 14D99
algebraic cycles, Chow groups, quadric bundles, motives, Chow--künneth decomposition