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Galois representations and Galois groups over Q
Arias De Reyna Dominguez, Sara; Armana, Cécile; Karemaker, Valentijn et al.
2015In Bertin, Marie José; Bucur, Alina; Feigon, Brooke et al. (Eds.) Women in Numbers Europe Research Directions in Number Theory
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Keywords :
Galois representation; inverse Galois problem over Q
Abstract :
[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].
Disciplines :
Mathematics
Author, co-author :
Arias De Reyna Dominguez, Sara ;  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
External co-authors :
yes
Language :
English
Title :
Galois representations and Galois groups over Q
Publication date :
2015
Event name :
Women in Numbers Europe
Event organizer :
Marie-José Bertin (Jussieu)
Alina Bucur (UCSD)
Brooke Feigon (City College of New York)
Leila Schneps (Jussieu)
Event place :
Marseille, France
Event date :
from 14-10-2013 to 18-10-2013
By request :
Yes
Audience :
International
Main work title :
Women in Numbers Europe Research Directions in Number Theory
Editor :
Bertin, Marie José
Bucur, Alina
Feigon, Brooke
Schneps, Leila
Publisher :
Springer
ISBN/EAN :
978-3-319-17986-5
Collection name :
Association for Women in Mathematics Series; 2
Pages :
191-205
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 24 July 2014

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