Wildly primitive extensions

TL;DR

This paper aims to provide a canonical parametrization of wildly ramified primitive extensions of local fields with finite residue fields, focusing on their unique properties and classifications.

Contribution

It introduces a new canonical parametrization method for wildly ramified primitive extensions of local fields, enhancing understanding of their structure.

Findings

Canonical parametrization of wildly ramified primitive extensions

Classification of such extensions based on ramification properties

Insights into the structure of local field extensions

Abstract

A finite separable extension of a field is called primitive if there are no intermediate extensions. The most interesting primitive extensions of a local field with finite residue field are the wildly ramified ones, and our aim here is to parametrise them in a canonical manner.