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

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Abstract

In 2007, Poonen (unpublished) studied the p-adic closure of a subgroup of rational points on a commutative algebraic group. More recently, Bellaïche asked the same question for the special case of Abelian varieties. These problems are p-adic analogues of a question raised earlier by 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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  1. Institut de Mathématiques de Jussieu—CNRS UMR 7586, Université Pierre et Marie Curie (Paris VI), 4, Place Jussieu, 75252, Paris Cedex 05, France

    Michel Waldschmidt

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Waldschmidt, M. On the p-adic closure of a subgroup of rational points on an Abelian variety. Afr. Mat. 22, 79–89 (2011). https://doi.org/10.1007/s13370-011-0012-3

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