Explicit determination of the images of the Galois representations attached to abelian surfaces with End(A)=\Z

Details Explicit determination of the images of the Galois representations attached to abelian surfaces with End(A)=\Z Explicit determination of the images of the Galois representations attached to abelian surfaces with End(A)=\Z

Publishing date

2001-10-24

URL

arxiv.org/abs/math/0110340v1

Science

Mathematics

Field

Number Theory

Type

Scientific paper

Abstract

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.

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