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Article Dans Une Revue Acta Arithmetica Année : 2016

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).
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Dates et versions

hal-01287556 , version 1 (17-02-2022)

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Sara Arias-De-Reyna, Cécile Armana, Valentijn Karemaker, Marusia Rebolledo, Lara Thomas, et al.. Large Galois images for Jacobian varieties of genus 3 curves. Acta Arithmetica, 2016, 174 (4), pp.101-132. ⟨10.4064/aa8250-4-2016⟩. ⟨hal-01287556⟩
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