Refined Swan conductors mod p of one-dimensional Galois representations

TL;DR

This paper introduces a new method for lifting the refined Swan conductor mod p for one-dimensional Galois representations using higher dimensional class field theory.

Contribution

It provides a novel approach to refine Swan conductors in the context of Galois representations with p-adic fields.

Findings

Defined a lifting of the refined Swan conductor mod p

Utilized higher dimensional class field theory for the construction

Enhanced understanding of ramification invariants in Galois theory

Abstract

For a character of the absolute Galois group of a complete discrete valuation field, we define a lifting of the refined Swan conductor, using higher dimensional class field theory.