### An analogue of a conjecture of Mazur a question in Diophantine approximation on tori, by Dipendra Prasad

Abstract: 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 $T$.

Dipendra Prasad <dprasad@mri.ernet.in>