Algebraic cycles and fibrations

By Charles Vial. Documenta Mathematica, 2012

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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 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/872a3ce0931adb6fe597fc592aa9496497eb490e