On the $p$-adic closure of a subgroup of rational points on an Abelian variety
Résumé
In 2007, B. Poonen (unpublished) studied the $p$-adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J.Bellaïche asked the same question for the special case of Abelian varieties. These problems are $p$-adic analogues of a question raised earlier by B. Mazur on the density of rational points for the real topology. For a simple Abelian variety over the field of rational numbers, we show that the actual $p$-adic rank is at least the third of the expected value.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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