Large Galois images for Jacobian varieties of genus 3 curves

2015/07/21 by Sara Arias‐de‐Reyna, Arias-de-Reyna, Sara, Cécile Armana +9
Computer Science · Mathematics · #11F80 #11G30 #11R32 #12F12 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1507.05913

openalex publication_date 2015/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Citations

• An explicit Jacobian of dimension 3 with maximal Galois action

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