Article
Large Galois images for Jacobian varieties of genus 3 curves
Author/s | Arias de Reyna Domínguez, Sara
Armana, Cécile Karemaker, Valentijn Rebolledo, Marusia Thomas, Lara Vila Oliva, Núria |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2016 |
Deposit Date | 2016-10-13 |
Published in |
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Abstract | Given a prime number ℓ ≥ 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 ρA,ℓ : GQ → GSp6 (Fℓ) attached to the ℓ-torsion of ... Given a prime number ℓ ≥ 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 ρA,ℓ : GQ → GSp6 (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 Sp6 (Fℓ). |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España Université de Franche-Comté |
Project ID. | info:eu-repo/grantAgreement/MTM2012-33830
BQR 2013 ANR-12-BS01-0002 |
Citation | Arias de Reyna Domínguez, S., Armana, C., Karemaker, V., Rebolledo, M., Thomas, L. y Vila Oliva, N. (2016). Large Galois images for Jacobian varieties of genus 3 curves. Acta Arithmetica, 174 (4), 339-366. |
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