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Large Galois images for Jacobian varieties of genus 3 curves
Arias De Reyna Dominguez, Sara; Armana, Cécile; Karemaker, Valentijn et al.


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Keywords :
Galois representation; inverse Galois problem over Q; Genus 3 curves
Abstract :
[en] 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, l) 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, l).
Disciplines :
Author, co-author :
Arias De Reyna Dominguez, Sara ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Armana, Cécile;  Université de Franche-Comté > Laboratoire de Mathématiques (LM-Besançon)
Karemaker, Valentijn;  Utrecht University
Rebolledo, Marusia;  Université Blaise Pascal - Clermont-Ferrand II > Laboratoire de Mathématiques
Thomas, Lara;  Université de Franche-Comté > Laboratoire de Mathématiques (LM-Besançon)
Vila, Núria;  University of Barcelona > Departament d'`Algebra
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Title :
Large Galois images for Jacobian varieties of genus 3 curves
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since 18 December 2015


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