Christopher Thornhill
Published 2011-03-11, updated 2012-01-31Version 2
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}).
Comments: 10 pages; revision; typos corrected; clarified ambiguities; changed numbering/naming of results; Prop. 2 replaced by Lemmas 6-11; some definitions altered to simplify presentation; small changes made to some proofs to correct errors (notably Props. 12 and 24); changes made to some proofs and results added to simplify/streamline arguments (notably Lemmas 9 and 15); new "thank you's" added
Galois extensions ramified only at one prime
On the existence of rotated $D_n$-lattices constructed via Galois extensions
On the number of certain Galois extensions of local fields
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