On totally ramified extensions of discrete valued fields

TL;DR

This paper provides a straightforward criterion to identify totally wild ramified valuations in Galois extensions of fields with characteristic p, using valuations of Artin-Schreier cosets, and demonstrates its application through example construction.

Contribution

It introduces a simple characterization of totally wild ramified valuations in Galois extensions of characteristic p fields, linking valuations of Artin-Schreier cosets to ramification.

Findings

Criterion effectively characterizes totally wild ramification

Application to construct new examples of ramified extensions

Simplifies analysis of ramification in characteristic p fields

Abstract

We give a simple characterization of the totally wild ramified valuations in a Galois extension of fields of characteristic p. This criterion involves the valuations of Artin-Schreier cosets of the F_{p^r}^\times-translation of a single element. We apply the criterion to construct some interesting examples.