Borne de hauteur semi-effective pour le problème de Mordell–Lang dans une variété abélienne

Abstract

Let X be a closed subscheme of an abelian variety on a number field. Let Z X denote the union of all translated positive dimensional abelian subvarieties contained in X. Faltings proved that the set of rational points on X∖Z X is finite. Moreover, if V→P is a family of closed subscheme of A, McQuillan gave an ineffective bound for the height of the rational points of each V p ∖Z V p . We extend the result of McQuillan to the case of Mordell–Lang plus Bogomolov problem and we give a semi-effective bound for the height of the rational points in V p ∖Z V p .