阿贝尔簇与希尔伯特域的伽罗瓦扩张
数论
2012-02-01 v2
摘要
在近期的一篇论文中，Moshe Jarden提出了一个猜想，后来被命名为Kuykian猜想，其内容为：如果A是定义在希尔伯特域K上的阿贝尔簇，那么K(A_{tor})/K的每一个中间域都是希尔伯特域。我们证明了该猜想对于K(A_{tor})中K的伽罗瓦扩张成立。
引用
@article{arxiv.1103.2333,
title = {Abelian Varieties and Galois Extensions of Hilbertian Fields},
author = {Christopher Thornhill},
journal= {arXiv preprint arXiv:1103.2333},
year = {2012}
}
备注
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