Article
Big monodromy theorem for abelian varieties over finitely generated fields
Author/s | Arias de Reyna Domínguez, Sara
Gajda, Wojciech J. Petersen, Sebastian |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2013-02 |
Deposit Date | 2016-10-13 |
Published in |
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Abstract | An abelian variety over a field K is said to have big monodromy, if the image of the Galois representation on ℓ-torsion points, for almost all primes ℓ, contains the full symplectic group. We prove that all abelian varieties ... An abelian variety over a field K is said to have big monodromy, if the image of the Galois representation on ℓ-torsion points, for almost all primes ℓ, contains the full symplectic group. We prove that all abelian varieties over a finitely generated field K with the endomorphism ring Z and semistable reduction of toric dimension one at a place of the base field K have big monodromy. We make no assumption on the transcendence degree or on the characteristic of K. This generalizes a recent result of Chris Hall. |
Project ID. | MTM2009-07024
GR 998/5-1 |
Citation | Arias de Reyna Domínguez, S., Gajda, W.J. y Petersen, S. (2013). Big monodromy theorem for abelian varieties over finitely generated fields. Journal of Pure and Applied Algebra, 217 (2), 218-229. |
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