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

Published online by Cambridge University Press:  04 December 2007

EMMANUELLE FROSSARD
EMMANUELLE FROSSARD
Affiliation:
Université de Paris-Sud, Département des mathématiques, Bˆ. 425, 91405 Orsay Cedex, France, e-mail: frossard@matups.fr
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Abstract

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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).

Keywords

Chow groupsalgebraic cyclesarthmetic finiteness theoremGalois cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 110 , Issue 2 , January 1998 , pp. 187 - 213
Copyright
© 1998 Kluwer Academic Publishers