Geodesic
Algebraic cycles and fibrations
Documenta mathematica, Tome 18 (2013), pp. 1521-1553.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $B$.
Classification : 14C15, 14C25, 14C05, 14D99
Keywords: algebraic cycles, Chow groups, quadric bundles, motives, Chow--künneth decomposition 
@article{DOCMA_2013__18__a3,
     author = {Vial, Charles},
     title = {Algebraic cycles and fibrations},
     journal = {Documenta mathematica},
     pages = {1521--1553},
     publisher = {mathdoc},
     volume = {18},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a3/}
}
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Vial, Charles. Algebraic cycles and fibrations. Documenta mathematica, Tome 18 (2013), pp. 1521-1553. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a3/