Densité de points et minoration de hauteur

We obtain a lower bound for the normalised height of a non-torsion subvariety V of a C.M. abelian variety. This lower bound is optimal in terms of the geometric degree of V, up to a power of a “log”. We thus extend the results of Amoroso and David on the same problem on a multiplicative group . We prove furthermore that the optimal lower bound (conjectured by David and Philippon) is a corollary of the conjecture of David and Hindry on the abelian Lehmerʹs problem. We deduce these results from a density theorem on the non-torsion points of V.