Abelian varieties over number fields, tame ramification and big Galois image
Given a natural number n ≥ 1 and a number field K, we show the existence of an integer ℓ0 such that for any prime number ℓ ≥ ℓ0, there exists a finite extension F/K, unramified in all places above ℓ, together with a principally polarized abelian variety A of dimension n over F such that the resultin...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47403 |
| Acceso en línea: | http://hdl.handle.net/11441/47403 https://doi.org/10.4310/MRL.2013.v20.n1.a1 |
| Access Level: | acceso abierto |
| Sumario: | Given a natural number n ≥ 1 and a number field K, we show the existence of an integer ℓ0 such that for any prime number ℓ ≥ ℓ0, there exists a finite extension F/K, unramified in all places above ℓ, together with a principally polarized abelian variety A of dimension n over F such that the resulting ℓ-torsion representation ρA,ℓ : GF → GSp(A[ℓ](F)) is surjective and everywhere tamely ramified. In particular, we realize GSp2n(Fℓ) as the Galois group of a finite tame extension of number fields F0/F such that F is unramified above ℓ. |
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