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Pré-Publication, Document De Travail Année : 2010

On the $p$-adic closure of a subgroup of rational points on an Abelian variety

Michel Waldschmidt
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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In 2007, B. Poonen (unpublished) studied the $p$-adic closure of a subgroup of rational points on a commutative algebraic group.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.
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hal-00549917 , version 1 (23-12-2010)

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  • HAL Id : hal-00549917 , version 1

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Michel Waldschmidt. On the $p$-adic closure of a subgroup of rational points on an Abelian variety. 2010. ⟨hal-00549917⟩
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