On Albanese torsors and the elementary obstruction

We show that the elementary obstruction to the existence of 0-cycles of degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed in terms of the Albanese 1-motives associated with dense open subsets of X. Arithmetic applications are given

Réduction des groupes algébriques commutatifs

We study a problem of constructing an algebraic torus (an abelian variety) over a p-adic field whose Ne Âron model would have a given connected commutative unipotent group as the identity component of its special fibre