Approximation on abelian varieties by its subgroups

2015/04/09 by Arash Rastegar, Rastegar, Arash
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1504.03367

openalex publication_date 2015/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce an algebro-geometric formulation for Faltings' theorem on diophantine approximation on abelian varieties using an improvement of Faltings-Wustholz observation over number fields. In fact, we prove that, for any geometrically irreducible sub-variety E of an abelian variety A and any finitely generated subgroup F of A(C) we have an estimate of the form d_v(E;x) >cH(x)^d for for some constant c where d_v(E;x) denotes the distance of a point x in F outside E and v is a place of K. This was proved before, only for F being the set of rational points of A over a number field.

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