Approximation diophantienne sur les variétés semi-abéliennes

Let A be a semi-abelian variety over , Γ a subgroup of of finite rank and X a subvariety of A which is not a translate of a semi-abelian subvariety of A. Work by P. Vojta and M. McQuillan shows that is not dense in X. B. Poonen has then conjectured that the same remains true if Γ is replaced by a fattening for a certain ε>0 where h is a canonical height. B. Poonen and S. Zhang have shown independently this to hold when A is almost split. On the other hand, the statement contains the Bogomolov property (with Γ=0) now proven by S. David and P. Philippon. In this paper, we prove Poonen's conjecture for any A. We also consider the slightly more general sets instead of Γ_ε. We use the case Γ=0 as well as a generalized Vojta inequality.