LOWER BOUNDS OF HEIGHTS ON ABELIAN-VARIETIES

In the following, we prove a lower bound for the Neron-Tat, height of an algebraic point of a principally polarized abelian variety defined over QBAR. This can be seen as a first approach of a generalisation of a conjecture of S. Lang, which was suggested by J. Silverman. Our lower bound depends on the logarithmic stable height of the variety and of an analytic invariant. This is the first lower bound which can go to infinity with the height of the variety. The proof of our result is based on transcendence methods.