# Refined ramification breaks in characteristic $p$

## TL;DR

This paper introduces an alternative way to define refined ramification breaks in characteristic p local fields and computes these breaks in specific cases using Artin-Schreier theory.

## Contribution

It provides a new definition for refined ramification breaks and applies Artin-Schreier theory to compute them in certain elementary abelian p-extensions.

## Key findings

- New definition for refined ramification breaks
- Explicit computation of breaks in special cases
- Application of Artin-Schreier theory

## Abstract

Let $K$ be a local field of characteristic $p$ and let $L/K$ be a totally ramified elementary abelian $p$-extension with a single ramification break $b$. Byott and Elder defined the refined ramification breaks of $L/K$, an extension of the usual ramification data. In this paper we give an alternative definition for the refined ramification breaks, and we use Artin-Schreier theory to compute both versions of the breaks in some special cases.