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Big monodromy theorem for abelian varieties over finitely generated fields

 

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Opened Access Big monodromy theorem for abelian varieties over finitely generated fields
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Author: Arias de Reyna Domínguez, Sara
Gajda, Wojciech J.
Petersen, Sebastian
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2013-02
Published in: Journal of Pure and Applied Algebra, 217 (2), 218-229.
Document type: Article
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 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.
Cite: 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.
Size: 298.3Kb
Format: PDF

URI: http://hdl.handle.net/11441/47408

DOI: 10.1016/j.jpaa.2012.06.010

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