Densité de points et minoration de hauteur

Details Densité de points et minoration de hauteur Densité de points et minoration de hauteur

2003-04-03

arxiv.org/abs/math/0304046v2

Mathematics

Number Theory

15 pages, proof of lemme 3 corrected

Scientific paper

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 $\mathbb{G}_m^n$. 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 $V$.

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