Abelian Varieties and Galois Extensions of Hilbertian Fields

Details Abelian Varieties and Galois Extensions of Hilbertian Fields Abelian Varieties and Galois Extensions of Hilbertian Fields

2011-03-11

arxiv.org/abs/1103.2333v2

Mathematics

Number Theory

10 pages; revision; typos corrected; clarified ambiguities; changed numbering/naming of results; Prop. 2 replaced by Lemmas 6-

Scientific paper

In a recent paper, Moshe Jarden proposed a conjecture, later named the
Kuykian conjecture, which states that if A is an abelian variety defined over a
Hilbertian field K, then every intermediate field of K(A_{tor})/K is
Hilbertian. We prove that the conjecture holds for Galois extensions of K in
K(A_{tor}).

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