2016-10-132016-10-132013Arias de Reyna Domínguez, S. y Kappen, C. (2013). Abelian varieties over number fields, tame ramification and big Galois image. Mathematical Research Letters, 20 (1), 1-17.1073-27801945-001Xhttp://hdl.handle.net/11441/47403Given 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.4310/MRL.2013.v20.n1.a1