### Explicit determination of the images of the Galois representations attached to abelian surfaces with End(A)=mathbb{Z}, by Luis V. Dieulefait

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 $\End(A)= \mathbb{Z}$ are as large as possible for
almost every prime. Our algorithm depends on the truth of Serre's conjecture for two
dimensional odd irreducible Galois representations. Assuming this conjecture we determine the finite set of primes with exceptional image.

Luis V. Dieulefait <luisd@mat.ub.es ; luisd@math.univ-paris13.fr>