Definable groups in topological fields with a generic derivation

TL;DR

This paper investigates definable groups within topological fields equipped with a generic derivation, establishing a connection between definable groups in the expanded language and topological groups in the original language using o-minimal structure techniques.

Contribution

It introduces a method to associate $ ext{L}_ ext{delta}$-definable groups with $ ext{L}$-definable topological groups in topological fields with a generic derivation.

Findings

Associates $ ext{L}_ ext{delta}$-definable groups with $ ext{L}$-definable topological groups.

Utilizes group configuration tools in o-minimal structures.

Provides a framework for understanding definable groups in topological fields with derivations.

Abstract

We continue the study of a class of topological $\mathcal{L}$-fields endowed with a generic derivation $\delta$, focussing on describing definable groups. We show that one can associate to an $\mathcal{L}_{\delta}$ definable group a type $\mathcal{L}$-definable topological group. We use the group configuration tool in o-minimal structures as developed by K. Peterzil.