Large Galois images for Jacobian varieties of genus 3 curves

Sara Arias-De-Reyna; Cécile Armana; Valentijn Karemaker; Marusia Rebolledo; Lara Thomas; Núria Vila

doi:10.4064/aa8250-4-2016

Large Galois images for Jacobian varieties of genus 3 curves

Sara Arias-De-Reyna
, Cécile Armana
, Valentijn Karemaker
, Marusia Rebolledo
, Lara Thomas
, Núria Vila

University of Seville
Université de Franche-Comté
Campus Universitaire des Cézeaux
Autonomous University of Barcelona

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Given a prime number , we construct an infinite family of three-dimensional abelian varieties over such that, for any in the family, the Galois representation attached to the -torsion of is surjective. Any such variety will be the Jacobian of a genus curve over whose respective reductions at two auxiliary primes are prescribed to provide us with generators of .

Original language	English
Pages (from-to)	339-366
Number of pages	28
Journal	Acta Arithmetica
Volume	174
Issue number	4
DOIs	https://doi.org/10.4064/aa8250-4-2016
Publication status	Published - 5 Aug 2016

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title = "Large Galois images for Jacobian varieties of genus 3 curves",

abstract = "Given a prime number , we construct an infinite family of three-dimensional abelian varieties over such that, for any in the family, the Galois representation attached to the -torsion of is surjective. Any such variety will be the Jacobian of a genus curve over whose respective reductions at two auxiliary primes are prescribed to provide us with generators of . ",

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T1 - Large Galois images for Jacobian varieties of genus 3 curves

AU - Arias-De-Reyna, Sara

AU - Armana, Cécile

AU - Karemaker, Valentijn

AU - Rebolledo, Marusia

AU - Thomas, Lara

AU - Vila, Núria

PY - 2016/8/5

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N2 - Given a prime number , we construct an infinite family of three-dimensional abelian varieties over such that, for any in the family, the Galois representation attached to the -torsion of is surjective. Any such variety will be the Jacobian of a genus curve over whose respective reductions at two auxiliary primes are prescribed to provide us with generators of .

AB - Given a prime number , we construct an infinite family of three-dimensional abelian varieties over such that, for any in the family, the Galois representation attached to the -torsion of is surjective. Any such variety will be the Jacobian of a genus curve over whose respective reductions at two auxiliary primes are prescribed to provide us with generators of .

UR - https://www.scopus.com/pages/publications/84983593575

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DO - 10.4064/aa8250-4-2016

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VL - 174

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JO - Acta Arithmetica

JF - Acta Arithmetica

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Large Galois images for Jacobian varieties of genus 3 curves

Abstract

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