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

2002/04/15 by Dipendra Prasad, Prasad, Dipendra · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Topological and Geometric Data Analysis #math.NT

paper · pdf · doi:10.48550/arxiv.math/0204359

arxiv created 2002/04/15 · openalex publication_date 2002/04/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Γ\backslash T(\Bbb R) where T is a torus defined over \Bbb Q, Γ an arithmetic subgroup such that Γ\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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