Abelian Varieties and Galois Extensions of Hilbertian Fields
Number Theory
2012-02-01 v2
Abstract
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}).
Cite
@article{arxiv.1103.2333,
title = {Abelian Varieties and Galois Extensions of Hilbertian Fields},
author = {Christopher Thornhill},
journal= {arXiv preprint arXiv:1103.2333},
year = {2012}
}
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