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

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

2010-07-27

arxiv.org/abs/1007.4725v1

Mathematics

Number Theory

19 pages ; en fran\c{c}ais/in French

Scientific paper

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.

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