Surjectivity of Galois representations associated with quadratic Q-curves

TL;DR

This paper establishes a uniform surjectivity result for Galois representations linked to non-CM Q-curves over imaginary quadratic fields, employing diverse mathematical tools and methods.

Contribution

It provides a new uniform surjectivity theorem for Galois representations of Q-curves over imaginary quadratic fields, extending previous results with novel techniques.

Findings

Proves uniform surjectivity for Galois representations of non-CM Q-curves.

Utilizes Mazur's method, isogeny theorems, and L-function estimates.

Extends understanding of Galois representations in the context of imaginary quadratic fields.

Abstract

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.