Generalized Differential Galois Theory

TL;DR

This paper develops a generalized Galois theory for differential fields with parameters, extending Kolchin's work, and demonstrates that all connected differential algebraic groups can serve as Galois groups of suitable differential field extensions.

Contribution

It introduces a broader Galois theory framework for differential fields with parameters, encompassing all connected differential algebraic groups as Galois groups.

Findings

All connected differential algebraic groups are Galois groups of some differential field extension.

The theory generalizes Kolchin's classical differential Galois theory.

Provides a unified approach to differential algebraic groups and Galois theory.

Abstract

A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field extension.