Abstract
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).
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