AN EFFECTIVE VERSION OF FALTINGS PRODUCT THEOREM

We give an explicit version of the Faltings' Product Theorem. It was f ormulated by Faltings in his paper [Fa], in order to prove a conjectur e of Lang on abelian varieties. The main ingredients are the multiplic ity estimates of [W] and the geometric as well as the arithmetic Bezou t's Theorem. We need to use the concept of height of a projective vari ety and we do it by considering the tools of Arakelov geometry.