Ramification Theory for Artin-Schreier Extensions of Valuation Rings

TL;DR

This paper extends classical ramification theory to more general valuation rings for Artin-Schreier extensions, introducing refined invariants and addressing the defect case.

Contribution

It generalizes ramification invariants to broader valuation rings and includes the treatment of the defect case, enhancing theoretical understanding.

Findings

Refined ramification invariants for Artin-Schreier extensions

Comparison of classical and new invariants

Handling of the defect case in ramification theory

Abstract

The goal of this paper is to generalize and refine the classical ramification theory of complete discrete valuation rings to more general valuation rings, in the case of Artin-Schreier extensions. We define refined versions of invariants of ramification in the classical ramification theory and compare them. Furthermore, we can treat the defect case.