English

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).

Keywords

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

R2 v1 2026-06-21T10:20:42.371Z