Indices of inseparability for elementary abelian p-extensions

TL;DR

This paper introduces a method to compute the indices of inseparability for elementary abelian p-extensions of local fields with characteristic p, refining ramification data with explicit formulas in certain cases.

Contribution

It provides a new computational approach for indices of inseparability in elementary abelian p-extensions, especially when the Galois group has a single ramification break.

Findings

Method for computing indices of inseparability using norm groups

Explicit formulas derived for specific cases

Enhanced understanding of ramification in elementary abelian p-extensions

Abstract

Let K be a local field whose residue field is a finite field of characteristic p, and let L/K be a finite totally ramified Galois extension. Fried and Heiermann defined the "indices of inseparability" of L/K, a refinement of the ramification data of L/K. We give a method for computing the indices of inseparability of the extension L/K in terms of the norm group N_{L/K}(L^*) in the case where K has characteristic p and Gal(L/K) is an elementary abelian p-group with a single ramification break. In some cases our methods lead to simple formulas for the indices of inseparability.