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arXiv · 1507.05913

Large Galois images for Jacobian varieties of genus 3 curves

Sara Arias-de-Reyna·Cécile Armana·Valentijn Karemaker·Marusia Rebolledo·Lara Thomas·Núria Vila
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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 \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).

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Sara Arias-de-Reyna, Cécile Armana, Valentijn Karemaker, Marusia Rebolledo, Lara Thomas, Núria Vila. 2015-07-21. Large Galois images for Jacobian varieties of genus 3 curves. https://arxiv.org/abs/1507.05913

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