Article
Tame Galois realizations of GSp4 (Fℓ) over Q
Author/s | Arias de Reyna Domínguez, Sara
Vila Oliva, Núria |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2011 |
Deposit Date | 2016-11-10 |
Published in |
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Abstract | 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 ... 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 ρℓ attached to the Tate module at ℓ of a suitable abelian surface. We need to choose the abelian varieties carefully in order to ensure that the image of ρℓ 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 provide tame Galois realizations of the desired symplectic groups. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Project ID. | AP-20040601
MTM2006-04895 |
Citation | Arias de Reyna Domínguez, S. y Vila Oliva, N. (2011). Tame Galois realizations of GSp4 (Fℓ) over Q. International Mathematics Research Notices, 2011 (9), 2028-2046. |
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