Formes linéaires de logarithmes effectives sur les variétés abéliennes

We prove new measures of linear independence of logarithms on an abelian variety defined over , which are totally explicit in function of the invariants of the abelian variety (dimension, Faltings height, degree of a polarization). Besides, except an extra-hypothesis on the algebraic point considered and a weaker numerical constant, we improve on earlier results (in particular David's lower bound). We also introduce into the main theorem an algebraic subgroup that leads to a great variety of different lower bounds. An important feature of the proof is the implementation of the slope method of Bost and some results of Arakelov geometry naturally associated with it.