Big monodromy theorem for abelian varieties over finitely generated fields

Details Big monodromy theorem for abelian varieties over finitely generated fields Big monodromy theorem for abelian varieties over finitely generated fields

2012-01-11

arxiv.org/abs/1201.2335v1

Mathematics

Algebraic Geometry

arXiv admin note: substantial text overlap with arXiv:1010.2444

Scientific paper

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.

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