Galois representation; inverse Galois problem over Q; Genus 3 curves
Résumé :
[en] Given a prime number l greater than or equal to 5, we construct an infinite family of three-dimensional abelian varieties over Q such that, for any A/Q in the family, the Galois representation \rho_{A, l}: Gal_Q -> GSp(6, l) attached to the l-torsion of A is surjective. Any such variety A will be the Jacobian of a genus 3 curve over Q whose respective reductions at two auxiliary primes we prescribe to provide us with generators of Sp(6, l).
Disciplines :
Mathématiques
Auteur, co-auteur :
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, Núria; University of Barcelona > Departament d'`Algebra
Langue du document :
Anglais
Titre :
Large Galois images for Jacobian varieties of genus 3 curves
