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

By Chris Hall. 2008

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Let K be a number field and A/K be a polarized abelian variety with absolutely trivial endomorphism ring. We show that if the Néron model of A/K has at least one fiber with potential toric dimension 1, then, for almost all rational primes ℓ, the Galois group of the splitting field of the ℓ‐torsion of A is GSp2g(ℤ/ℓ).

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4ad0caa68f44158ef64437cf4427ecdddf089461