On uniform lower bound of the Galois images associated to elliptic curves
نویسندگان
چکیده
Résumé. Soit p un nombre premier et K un corps de nombres. Soit ρE,p : GK −→ Aut(TpE) ∼= GL2(Zp) la représentation Galoisienne donnée par l’action du groupe de Galois sur le module de Tate p-adique d’une courbe elliptique E définie sur K. Serre a prouvé que l’image de ρE,p est ouverte si E n’a pas de multiplication complexe. Pour E une courbe elliptique définie sur K et dont l’invariant j n’appartient pas à un ensemble fini exceptionnel (qui est non explicite cependant), nous donnons une minoration uniforme et explicite de la taille de l’image de ρE,p.
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