Galois representations and Galois groups over Q

Arias De Reyna Dominguez, Sara; Armana, Cécile; Karemaker, Valentijn; Rebolledo, Marusia; Thomas, Lara; Vila Oliva, Núria

doi:10.1007/978-3-319-17987-2

Reference : Galois representations and Galois groups over Q


	Document type :	Scientific congresses, symposiums and conference proceedings : Paper published in a book
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/17505

Title :	Galois representations and Galois groups over Q
Language :	English
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]
Publication date :	2015
Main document title :	Women in Numbers Europe Research Directions in Number Theory
Editor :	Bertin, Marie José
	Bucur, Alina
	Feigon, Brooke
	Schneps, Leila
Publisher :	Springer
Collection and collection volume :	Association for Women in Mathematics Series; 2
Pages :	191-205
Peer reviewed :	Yes
On invitation :	Yes
Audience :	International
ISBN :	978-3-319-17986-5
Event name :	Women in Numbers Europe
Event date :	from 14-10-2013 to 18-10-2013
Event organizer :	Marie-José Bertin (Jussieu)
	Alina Bucur (UCSD)
	Brooke Feigon (City College of New York)
	Leila Schneps (Jussieu)
Event place (city) :	Marseille
Event country :	France
Keywords :	[en] 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].
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/17505
DOI :	10.1007/978-3-319-17987-2

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