Big monodromy theorem for abelian varieties over finitely generated fields

2012/01/11 by Arias-de-Reyna, Sara, Gajda, Wojciech, Petersen, Sebastian
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1201.2335

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 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.

Related

• Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion
• Big symplectic or orthogonal monodromy modulo l
• Families of abelian varieties and large Galois images
• The monodromy of families of subvarieties on abelian varieties
• Monodromy groups of Jacobians with definite quaternionic multiplication