On the Hasse-Arf property of local fields

Abstract

Let $F/K$ be a finite Galois totally & wildly ramified extension of complete discrete valuation fields. We say that the extension has the Hasse-Arf property if the ramification jumps in upper numbering are integers. We give necessary defining equations for $F$ in terms of the ramification jumps. In order for the Hasse-Arf property to hold, these equations become very strict. We prove that the last assertion is an equivalence condition, thus in terms of these defining equations, the Hasse-Arf property becomes an equivalence condition.

arXiv comment15 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