The p-adic closure of a subgroup of rational points on a commutative algebraic group
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(Qp). We formulate a guess for the dimension of the closure of Gamma in G(Qp), and show that its correctness for certain tori is equivalent to Leopoldt's conjecture.
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