Proof of Serge Lang's Heights Conjecture and an almost optimal Bound for the Torsion of Elliptic Curves

Abstract

This paper focuses on the proof of Serge Lang's Heights Conjecture in a form that is completely effective. As a complementary result the author provides a new proof of Mazur-Merel theorem about a bound for the torsion of elliptic curves in terms of the degree of the ground field and improves the known result by providing a small polynomial bound in terms of this degree. (Submitted)