Large Galois images for Jacobian varieties of genus 3 curves
Résumé
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,Fl) 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,Fl).
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)