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arXiv · 1204.5441

Abelian varieties over number fields, tame ramification and big Galois image

Sara Arias-de-Reyna·Christian Kappen
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Abstract

Given a natural number n and a number field K, we show the existence of an integer \ell_0 such that for any prime number \ell\geq \ell_0, there exists a finite extension F/K, unramified in all places above \ell, together with a principally polarized abelian variety A of dimension n over F such that the resulting \ell-torsion representation \rho_{A,\ell} from G_F to GSp(A[\ell](\bar{F})) is surjective and everywhere tamely ramified. In particular, we realize GSp_{2n}(\mathbb{F}_\ell) as the Galois group of a finite tame extension of number fields F'/F such that F is unramified above \ell.

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Sara Arias-de-Reyna, Christian Kappen. 2012-04-24. Abelian varieties over number fields, tame ramification and big Galois image. https://arxiv.org/abs/1204.5441

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