Valuation theoretic and model theoretic aspects of local uniformization

TL;DR

This paper surveys valuation theory and model theory related to local uniformization in positive characteristic, exploring their connections with the defect phenomenon in valued fields.

Contribution

It provides a comprehensive overview of valuation and model theoretic approaches to local uniformization and their interplay with the defect in positive characteristic.

Findings

Valuation theoretical approach to local uniformization in positive characteristic.

Connections between model theory of valued fields and uniformization.

Insights into the valuation phenomenon of defect.

Abstract

This paper gives a survey on a valuation theoretical approach to local uniformization in positive characteristic, the model theory of valued fields in positive characteristic, and their connection with the valuation theoretical phenomenon of defect.