Big monodromy theorem for abelian varieties over finitely generated fields
Algebraic Geometry
2012-01-12 v1 Representation Theory
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.
Keywords
Cite
@article{arxiv.1201.2335,
title = {Big monodromy theorem for abelian varieties over finitely generated fields},
author = {Sara Arias-de-Reyna and Wojciech Gajda and Sebastian Petersen},
journal= {arXiv preprint arXiv:1201.2335},
year = {2012}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1010.2444