Compositio Mathematica

Groupe de Chow de dimension zéro des fibrations en variétés de Severi–Brauer

a1 Université de Paris-Sud, Département des mathématiques, B^. 425, 91405 Orsay Cedex, France, e-mail:

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We study here the O-dimension Chow group of some particular smooth varieties which are fibrations over curves (i.e. are equipped with a proper, surjective morphism over a smooth curve). We obtain finiteness results for fibrations, whose generic fibres are Severi-Brauer varieties of squarefree index, when the group field is a number field (or in some particular cases a finitely generated field over Q).

Key Words: Chow groups; algebraic cycles; arthmetic finiteness theorem; Galois cohomology.