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arXiv · 1203.2650

Algebraic cycles and fibrations

Charles Vial
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Abstract

Let $f : X -> B$ 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 fibers 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 motive of $X$ is "built" from the motives of varieties of dimension less than the dimension of $B$.

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Charles Vial. 2012-03-12. Algebraic cycles and fibrations. https://arxiv.org/abs/1203.2650

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