Geodesic
The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields
Bjorn Poonen1 ; José Felipe Voloch2
1 Massachusetts Institute of Technology, Department of Mathematics, Building 2, Room 244, 77 Massachusetts Avenue, Cambridge MA 02139-4307, United States
2 The University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin TX 78712, United States
Annals of mathematics, Tome 171 (2010) no. 1, pp. 511-532.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that for a large class of subvarieties of abelian varieties over global function fields, the Brauer-Manin condition on adelic points cuts out exactly the rational points. This result is obtained from more general results concerning the intersection of the adelic points of a subvariety with the adelic closure of the group of rational points of the abelian variety.
DOI : 10.4007/annals.2010.171.511

Bjorn Poonen 1 ; José Felipe Voloch 2

1 Massachusetts Institute of Technology, Department of Mathematics, Building 2, Room 244, 77 Massachusetts Avenue, Cambridge MA 02139-4307, United States
2 The University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin TX 78712, United States 
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Bjorn Poonen; José Felipe Voloch. The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Annals of mathematics, Tome 171 (2010) no. 1, pp. 511-532. doi : 10.4007/annals.2010.171.511. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.511/

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