Reference : Tame Galois realizations of $ GSp_4(\Bbb F_łl)$ over $\Bbb Q$
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Tame Galois realizations of $ GSp_4(\Bbb F_łl)$ over $\Bbb Q$
Arias De Reyna Dominguez, Sara mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Vila, Núria [University of Barcelona > Departament d’Àlgebra i Geometria]]
International Mathematics Research Notices
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[en] In this paper, we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic l> 3 as the Galois group of a tamely ramified Galois extension of Q. The strategy is to consider the Galois representation ρ_l attached to the Tate module at l of a suitable abelian surface. We need to choose the abelian surfaces carefully in order to ensure that the image of ρ_l is large and simultaneously maintain a control on the ramification of the corresponding Galois extension. We obtain an explicit family of curves of genus 2 such that the Galois representation attached to the l-torsion points of their Jacobian varieties provides tame Galois realizations of the desired symplectic groups.
2806556 (2012f:12010)

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