An analogue of a conjecture of Mazur a question in Diophantine approximation on tori

Details An analogue of a conjecture of Mazur a question in Diophantine approximation on tori An analogue of a conjecture of Mazur a question in Diophantine approximation on tori

2002-04-15

arxiv.org/abs/math/0204359v1

Mathematics

Number Theory

Scientific paper

B. Mazur has considered the question of density in the Euclidean topology of the set of ${\Bbb Q}$-rational points on a variety $X$ defined over ${\Bbb Q}$, in particular for Abelian varieties. In this paper we consider the question of closures of the image of finitely generated subgroups of $T({\Bbb Q})$ in $\Gamma \backslash T({\Bbb R})$ where $T$ is a torus defined over ${\Bbb Q}$, $\Gamma$ an arithmetic subgroup such that $\Gamma \backslash T({\Bbb R})$ is compact. Assuming Schanuel's conjecture, we prove that the closures correspond to sub {\it algebraic} tori of $T$.

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