Very strong approximation for certain algebraic varieties

Qing Liu 1 Fei Xu
1 Équipe Théorie des Nombres
IMB - Institut de Mathématiques de Bordeaux
Abstract : Let F be a global field. In this work, we show that the Brauer-Manin condition on adelic points for subvarieties of a torus T over F cuts out exactly the rational points, if either F is a function field or, if F is the field of rational numbers and T is split. As an application, we prove a conjecture of Harari-Voloch over global function fields which states, roughly speaking, that on any rational hyperbolic curve, the local integral points with the Brauer-Manin condition are the global integral points. Finally we prove for tori over number fields a theorem of Stoll on adelic points of zero-dimensional subvarieties in abelian varieties.
Type de document :
Article dans une revue
Mathematische Annalen, Springer Verlag, 2015, 363 (3), pp.701-731. 〈http://link.springer.com/journal/208〉
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https://hal.archives-ouvertes.fr/hal-01257924
Contributeur : Qing Liu <>
Soumis le : lundi 18 janvier 2016 - 14:12:41
Dernière modification le : jeudi 11 janvier 2018 - 06:26:36

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  • HAL Id : hal-01257924, version 1
  • ARXIV : 1405.1988

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Qing Liu, Fei Xu. Very strong approximation for certain algebraic varieties. Mathematische Annalen, Springer Verlag, 2015, 363 (3), pp.701-731. 〈http://link.springer.com/journal/208〉. 〈hal-01257924〉

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