Generalized Vojta inequality. (Inégalité de Vojta généralisée.) (French) Zbl 1136.11043

A crucial step in Vojta’s proof of the Mordell conjecture is an inequality on heights. In the paper under review the author presents a generalization of this inequality, more flexible and suitable for many applications. Among these, the author indicates two results: the proof of the Mordell-Lang plus Bogomolov statement for semiabelian varieties conjectured by Poonen [G. Rémond, “Approximation diophantienne sur les variétés semi-abéliennes”, Ann. Sci. Éc. Norm. Supér. (4) 36, No. 2, 191–212 (2003; Zbl 1081.11053)] and the proof of a more uniform statement of the Lang conjecture on abelian varieties [G. Rémond and E. Viada, “Problème de Mordell-Lang modulo certaines sous-variétés abéliennes”, Int. Math. Res. Not. 2003, No. 35, 1915–1931 (2003; Zbl 1072.11038)]. It is to be remarked that the main theorem of the paper is a statement about varieties defined over \({\bar \mathbb Q}\) and does not depend on the number field on which a variety is defined.


11G50 Heights
11G35 Varieties over global fields
14G25 Global ground fields in algebraic geometry
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