Purely inseparable extensions and ramification filtrations

TL;DR

This paper studies how ramification filtrations of Galois groups change under purely inseparable extensions in positive characteristic fields, and explores functoriality of characteristic forms.

Contribution

It introduces a detailed analysis of the behavior of ramification filtrations and characteristic forms under purely inseparable extensions in positive characteristic.

Findings

Ramification filtrations shift predictably under purely inseparable extensions

Functoriality properties of characteristic forms are established

Provides new insights into Galois group structures in positive characteristic

Abstract

In this article, we investigate the shift of Abbes and Saito's ramification filtrations of the absolute Galois group of a complete discrete valuation field of positive characteristic under a purely inseparable extension. We also study a functoriality property for characteristic forms.