Densité de points et minoration de hauteur

الأصل · EN

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 F. Amoroso and S. David on the same problem on a multiplicative group Gₘⁿ. We prove furthermore that the optimal lower bound (conjectured by S. David and P. Philippon) is a corollary of the conjecture of S. David and M. Hindry on the abelian Lehmer's problem. We deduce these results from a density theorem on the non-torsion points of V.