Large Galois images for Jacobian varieties of genus 3 curves
Publication date
2016-08-05
Authors
Arias-De-Reyna, Sara
Armana, Cécile
Karemaker, Valentijn
Rebolledo, Marusia
Thomas, Lara
Vila, Núria
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Article
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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 .
Keywords
Taverne, Algebra and Number Theory
Citation
Arias-De-Reyna, S, Armana, C, Karemaker, V, Rebolledo, M, Thomas, L & Vila, N 2016, 'Large Galois images for Jacobian varieties of genus 3 curves', Acta Arithmetica, vol. 174, no. 4, pp. 339-366. https://doi.org/10.4064/aa8250-4-2016