On Galois representations with large image

A Note on Galois Representations with Big Image

Deformation of Outer Representations of Galois Group

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...

The large sieve and Galois representations

We describe a generalization of the large sieve to situations where the underlying groups are nonabelian, and give several applications to the arithmetic of abelian varieties. In our applications, we sieve the set of primes via the system of representations arising from the Galois action on the torsion points of an abelian variety. The resulting upper bounds require explicit character sum calcu...

On the Image of Λ-adic Galois Representations

We explore the question of how big the image of a Galois representation attached to a Λ-adic modular form with no complex multiplication is and show that for a “generic” set of Λ-adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all but a density 0 subset have large image.

On three-dimensional Galois representations

We give an irreducibility criterion for the Galois images of compatible l-adic systems of Galois representations. We apply this to the l-adic realizations of the van Geemen-Top motive M and prove an analogue of Serre’s theorem for M.