ALGEBRAIC CYCLES AND FIBRATIONS

作者：Vial Charles^*

来源：Documenta Mathematica, 2013, 18: 1521-1553.

DOI：10.4171/dm/435

• Algebraic cycles
• Chow groups
• quadric bundles
• motives
• Chow-Kunneth decomposition

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.

• 出版日期2013