Galois representations and Galois groups over Q
Abstract
In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve and let J(C) be the associated Jacobian variety. Assume that there exists a prime p such that J(C) has semistable reduction with toric dimension 1 at p. We provide an algorithm to compute a list of primes l (if they exist) such that the Galois representation attached to the l-torsion of J(C) is surjective onto the group GSp(2n, l). In particular we realize GSp(6, l) as a Galois group over Q for all primes l in [11, 500000].
Cite
@article{arxiv.1407.5802,
title = {Galois representations and Galois groups over Q},
author = {Sara Arias-de-Reyna and Cécile Armana and Valentijn Karemaker and Marusia Rebolledo and Lara Thomas and Núria Vila},
journal= {arXiv preprint arXiv:1407.5802},
year = {2014}
}
Comments
Minor changes. 13 pages. This paper contains results of the collaboration started at the conference Women in numbers - Europe, (October 2013), by the working group "Galois representations and Galois groups over Q"