Reference : Galois representations and Galois groups over Q
Scientific congresses, symposiums and conference proceedings : Paper published in a book
Physical, chemical, mathematical & earth Sciences : Mathematics
Galois representations and Galois groups over Q
Arias De Reyna Dominguez, Sara mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Armana, Cécile [Université de Franche-Comté > Laboratoire de Mathématiques (LM-Besançon)]
Karemaker, Valentijn [Utrecht University]
Rebolledo, Marusia [Université Blaise Pascal - Clermont-Ferrand II > Laboratoire de Mathématiques]
Thomas, Lara [Université de Franche-Comté > Laboratoire de Mathématiques (LM-Besançon)]
Vila Oliva, Núria [University of Barcelona > Departament d'`Algebra]
Women in Numbers Europe Research Directions in Number Theory
Bertin, Marie José
Bucur, Alina
Feigon, Brooke
Schneps, Leila
Association for Women in Mathematics Series; 2
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)
[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].

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