Algebraic cycles and fibrations

  • Charles Vial

    DPMMS University of Cambridge Wilberforce Road Cambridge CB3 0WB UK
Algebraic cycles and fibrations cover
Download PDF

This article is published open access.


Let f:XBf: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 XX in terms of the Chow groups of BB and of the fibres of ff. One of the applications concerns quadric bundles. When XX and BB are smooth projective and when ff is a flat quadric fibration, we show that the Chow motive of XX is «built» from the motives of varieties of dimension less than the dimension of BB.

Cite this article

Charles Vial, Algebraic cycles and fibrations. Doc. Math. 18 (2013), pp. 1521–1553

DOI 10.4171/DM/435