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For varieties over global fields, weak approximation in the space of adelicpoints can fail. For a subvariety of an abelian variety one expects thisfailure is always explained by a finite descent obstruction, in the sense thatthe rational points should be dense in the set of (modified) adelic pointssurviving finite descent. We show that this follows from the a priori weakerassumption that finite descent is the only obstruction to the existence ofrational points. We also prove a similar statement for the obstruction comingfrom the Mordell-Weil sieve.

Weak approximation versus the Hasse principle for subvarieties of abelian varieties