An ultrametric space of Eisenstein polynomials and ramification theory

TL;DR

This paper introduces a non-Archimedean metric on Eisenstein polynomials over local fields to determine when they define the same extension, leveraging ramification theory for the criterion.

Contribution

It develops a new criterion based on a non-Archimedean metric to compare Eisenstein polynomials in the context of ramification theory.

Findings

Provides a metric-based criterion for polynomial extension equivalence

Connects ramification theory with polynomial metric spaces

Enhances understanding of Eisenstein polynomial classification

Abstract

We give a criterion whether given Eisenstein polynomials over a local field K define the same extension over K in terms of a certain non-Archimedean metric on the set of polynomials. The criterion and its proof depend on ramification theory.