Mathematische Annalen

, Volume 340, Issue 4, pp 805–838

On Albanese torsors and the elementary obstruction


DOI: 10.1007/s00208-007-0170-7

Cite this article as:
Wittenberg, O. Math. Ann. (2008) 340: 805. doi:10.1007/s00208-007-0170-7


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.

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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsRice UniversityHoustonUSA