Ramification groups of coverings and valuations

TL;DR

This paper presents a scheme-theoretic approach to constructing ramification group filtrations for Galois coverings, accommodating non-discrete valuations with certain normalization conditions.

Contribution

It introduces a new purely scheme-theoretic method for defining ramification groups that does not require discrete valuations, broadening the applicability of ramification theory.

Findings

Provides a scheme-theoretic construction of ramification filtrations

Applicable to valuations that are not necessarily discrete

Requires normalizations to be locally complete intersection

Abstract

We give a purely scheme theoretic construction of the filtration by ramification groups of the Galois group of a covering. The valuation need not be discrete but the normalizations are required to be locally of complete intersection.