Women in Numbers Europe Research Directions in Number Theory
Bertin, Marie José
Bucur, Alina
Feigon, Brooke
Schneps, Leila
Springer
Association for Women in Mathematics Series; 2
191-205
Yes
Yes
International
978-3-319-17986-5
Women in Numbers Europe
from 14-10-2013 to 18-10-2013
Marie-José Bertin (Jussieu)
Alina Bucur (UCSD)
Brooke Feigon (City College of New York)
Leila Schneps (Jussieu)
Marseille
France
[en] Galois representation ; inverse Galois problem over Q
[en] 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].