Large Galois images for Jacobian varieties of genus 3 curves

Abstract

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 ρ_{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).

20 pages. Minor modifications, examples added. To appear in Acta Arithmetica

References in corpus (2)

• An explicit Jacobian of dimension 3 with maximal Galois action
• Residual Representations of Semistable Principally Polarized Abelian Varieties

Cited by in corpus (1)

• Surjectivity of Galois Representations in Rational Families of Abelian Varieties