Separably closed fields and contractive Ore modules

TL;DR

This paper studies valued fields with a Frobenius map as valued modules over an Ore ring, proving quantifier elimination in an expanded language that includes p-basis components and valuation group chains.

Contribution

It introduces a new framework for valued fields with a Frobenius map as valued modules over an Ore ring and establishes quantifier elimination in this setting.

Findings

Quantifier elimination for separably closed valued fields with Frobenius map

Development of a module-theoretic framework for valued fields with difference operators

Extension of language with p-basis components and valuation group chains

Abstract

We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented with functions yielding components for a p-basis and a chain of subgroups indexed by the valuation group.