Surjectivity of Galois representations associated with quadratic Q-curves

Samuel Le Fourn (1, 2)

1 Équipe Théorie des Nombres
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We prove in this paper an uniform surjectivity result for Galois representations associated with non-CM $\mathbb{Q}$-curves over imaginary quadratic fields, using various tools for the proof, such as Mazur's method, isogeny theorems, Runge's method and analytic estimates of sums of $L$-functions.

Mots clés: Runge's method.; Runge's method; Q-curves; isogeny theorems; Serre's uniformity problem; Galois representations

Domaines: Théorie des nombres [math.NT]

Samuel Le Fourn. Surjectivity of Galois representations associated with quadratic Q-curves. Mathematische Annalen, 2016, 365 (1-2), pp.173-214. ⟨10.1007/s00208-015-1269-x⟩. ⟨hal-00801781v1⟩