Article
Abelian varieties over number fields, tame ramification and big Galois image
Author/s | Arias de Reyna Domínguez, Sara
Kappen, Christian |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2013 |
Deposit Date | 2016-10-13 |
Published in |
|
Abstract | 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 ... 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Project ID. | MTM2009-07024 |
Citation | Arias 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. |
Files | Size | Format | View | Description |
---|---|---|---|---|
Abelian varieties over number ... | 213.6Kb | [PDF] | View/ | |