An open image theorem for a general class of abelian varieties
Number Theory
2014-02-26 v1
Abstract
Let K be a number field and A/K be a polarized abelian variety with absolutely trivial endomorphism ring. We show that if the Neron model of A/K has at least one fiber with potential toric dimension one, then for almost all rational primes ell, the Galois group of the splitting field of the ell-torsion of A is GSp_{2g}(Z/ell).
Cite
@article{arxiv.0803.1682,
title = {An open image theorem for a general class of abelian varieties},
author = {Chris Hall},
journal= {arXiv preprint arXiv:0803.1682},
year = {2014}
}
Comments
10 pages; appendix by Emmanuel Kowalski