局域域的 Hasse-Arf 性质研究
数论
2025-04-21 v1
摘要
设 为完备离散价值域的有限伽罗瓦全大ramification 扩张。若扩张的上编号中的ramification jump 为整数，则称该扩张具有 Hasse-Arf 性质。我们给出 由ramification jump 决定的必要定义方程。为使 Hasse-Arf 性质成立，这些方程变得非常严格。我们证明，最后这一断言是等价条件，因此从这些定义方程来看，Hasse-Arf 性质也成为等价条件。
引用
@article{arxiv.2504.13606,
title = {On the Hasse-Arf property of local fields},
author = {Ioannis Tsouknidas},
journal= {arXiv preprint arXiv:2504.13606},
year = {2025}
}
备注
15 pages. It is the analog of arXiv:2312.12753 for local fields. Compared to it, several assumptions have been removed and some examples added. It is a work in progress. Comments are welcome