Approximation on abelian varieties by its subgroups
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 dv(E;x) >cH(x)d for for some constant c where dv(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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