Résultats quantitatifs d'indépendance algébrique pour les groupes algébriques

Abstract

The main theorem of this paper is a quantitative result on the algebraic independence of numbers related to the exponential map of a commutative algebraic group defined over a number field. The qualitative version of this theorem improves an earlier result of M. Waldschmidt. In the elliptic case we improve upon previous lower bounds for the transcendence degree over Q of families of the type { P ( x iy j ), i, j} or { y j , P ( x iy j ), i, j} where P is a Weierstrass elliptic curve defined over Q.