Tame Galois realizations of GSp4 (Fℓ) over Q
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 abe...
| Authors: | , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2011 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/48442 |
| Online Access: | http://hdl.handle.net/11441/48442 https://doi.org/10.1093/imrn/rnq144 |
| Access Level: | Open access |
| Summary: | 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. |
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