Trace map and regularity of finite extensions of a DVR

TL;DR

This paper explores how the regularity of finite flat extensions of discrete valuation rings can be characterized through the properties of their trace maps, providing a new perspective on their structure.

Contribution

It introduces a novel interpretation linking regularity of finite flat extensions of DVRs to their trace maps, offering a new criterion for regularity.

Findings

Regularity characterized by trace map properties

Provides criteria for regularity of finite flat extensions

Connects algebraic structure with trace map behavior

Abstract

We interpret the regularity of a finite and flat extension of a discrete valuation ring in terms of the trace map of the extension.