Equivalence of Valued Fields with Valuation Preserving Automorphism

TL;DR

This paper advances the understanding of valued fields with valuation-preserving automorphisms by weakening previous assumptions and characterizes the induced structures in certain cases, enhancing the theoretical framework of valued difference fields.

Contribution

It weakens assumptions on residue difference fields and determines induced structures in equicharacteristic zero cases, extending prior results.

Findings

Weakened assumptions on residue difference fields.

Determined induced structures in equicharacteristic zero.

Extended theoretical understanding of valued difference fields.

Abstract

We improve results of Belair, Macintyre, and Scanlon on valued fields with a valuation preserving automorphism by weakening their assumptions on the residue difference field. In the equicharacteristic zero case we also determine the induced structure on the residue difference field and the value group.