Borne uniforme pour les homothéties dans l'image de Galois associée aux courbes elliptiques

Abstract

Let K be a fixed number field and G its absolute Galois group. We give a bound C(K), depending only on the degree, the class number and the discriminant of K, such that for any elliptic curve E defined over K and any prime number p strictly larger than C(K), the image of the representation of G attached to the p-torsion points of E contains a subgroup of homotheties of index smaller than 12.

19 pages ; en français/in French