k-Isomorphism Classes of Local Field Extensions

TL;DR

This paper classifies k-isomorphism classes of totally ramified separable extensions of degree p over local fields of characteristic p, extending previous work on Galois extensions.

Contribution

It provides a set of representatives for all such extensions, broadening the understanding of local field extension classifications.

Findings

Identifies representatives for k-isomorphism classes

Extends classification from Galois to all separable extensions

Enhances understanding of ramified extensions in characteristic p

Abstract

Let K be a local field of characteristic p with perfect residue field k. In this paper we find a set of representatives for the k-isomorphism classes of totally ramified separable extensions L/K of degree p. This extends work of Klopsch, who found representatives for the k-isomorphism classes of totally ramified Galois extensions L/K of degree p.