, Volume 340, Issue 4, pp 805-838
Date: 18 Oct 2007

On Albanese torsors and the elementary obstruction

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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.