Large Galois images for Jacobian varieties of genus 3 curves
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 ove...
| Autores: | , , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47411 |
| Acceso en línea: | http://hdl.handle.net/11441/47411 https://doi.org/10.4064/aa8250-4-2016 |
| Access Level: | acceso abierto |
| Palabra clave: | Galois representations Abelian varieties Genus 3 curves |
| Sumario: | 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). |
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