The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields


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.


Bjorn Poonen

Massachusetts Institute of Technology, Department of Mathematics, Building 2, Room 244, 77 Massachusetts Avenue, Cambridge MA 02139-4307, United States

José Felipe Voloch

The University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin TX 78712, United States