In a previous article, we have proved a result asserting the existence of a compatible family of Galois representations containing a given crystalline irreducible odd two-dimensional representation.… (More)

We give an effective version of a result reported by Serre asserting that the images of the Galois representations attached to an abelian surface with End(A) = Z are as large as possible for almost… (More)

We address the problem of the determination of the images of the Galois representations attached to genus 2 Siegel cusp forms of level 1 having multiplicity one. These representations are symplectic.… (More)

This note provides an insight to the diophantine properties of abelian surfaces with quaternionic multiplication over number fields. We study the fields of definition of the endomorphisms on these… (More)

We prove the following uniformity principle: if one of the Galois representations in the family attached to a genus two Siegel cusp form of weight k > 3, “semistable” and with multiplicity one, is… (More)

We give a method to solve generalized Fermat equations of type x 4+y4 = qz, for some prime values of q and every prime p bigger than 13. We illustrate the method by proving that there are no… (More)

This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves… (More)

In this paper, we are interested in solving the Fermat-type equations x5 + y5 = dzp, where d is a positive integer and p a prime number ≥ 7. We describe a new method based on modularity theorems… (More)