The p-adic closure of a subgroup of rational points on a commutative algebraic group

Bjorn Poonen

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arXiv · 0711.5028

The p-adic closure of a subgroup of rational points on a commutative algebraic group

Bjorn Poonen

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Abstract

Let G be a commutative algebraic group over Q. Let Gamma be a subgroup of G(Q) contained in the union of the compact subgroups of G(Q_p). We formulate a guess for the dimension of the closure of Gamma in G(Q_p), and show that its correctness for certain tori is equivalent to Leopoldt's conjecture.

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Bjorn Poonen. 2007-11-30. The p-adic closure of a subgroup of rational points on a commutative algebraic group. https://arxiv.org/abs/0711.5028

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