Reference : Large Galois images for Jacobian varieties of genus 3 curves
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Physical, chemical, mathematical & earth Sciences : Mathematics
Large Galois images for Jacobian varieties of genus 3 curves
Arias De Reyna Dominguez, Sara mailto [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]
[en] Galois representation ; inverse Galois problem over Q ; Genus 3 curves
[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).
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