Hasse 范数原理的显式方法及其在 $A_n$ 与 $S_n$ 扩张中的应用
数论
2021-01-07 v2
摘要
设 为一个数域扩张。我们描述了用于计算 的 Hasse 范数原理的障碍以及范数一元环面 的弱逼近缺陷的理论结果和计算方法。我们将这些技术应用于：当 的正规闭包具有对称或交错 Galois 群时，给出 Hasse 范数原理的障碍与弱逼近缺陷的显式可计算公式。
关键词
引用
@article{arxiv.1906.03730,
title = {Explicit methods for the Hasse norm principle and applications to $A_n$ and $S_n$ extensions},
author = {André Macedo and Rachel Newton},
journal= {arXiv preprint arXiv:1906.03730},
year = {2021}
}
备注
43 pages, final version. Major changes, including a restructure of the paper and the addition of a geometric interpretation of the first obstruction to the HNP, which improved several results and proofs. To appear in Math. Proc. Camb. Philos. Soc