  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.
