An open image theorem for a general class of abelian varieties

Details An open image theorem for a general class of abelian varieties An open image theorem for a general class of abelian varieties

2008-03-11

arxiv.org/abs/0803.1682v1

Mathematics

Number Theory

10 pages; appendix by Emmanuel Kowalski

Scientific paper

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).

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