Iterative Differential Embedding Problems in positive Characteristic

TL;DR

This paper proves that all iterative differential embedding problems over certain algebraic function fields in positive characteristic with algebraically closed constants have proper solutions, advancing the understanding of differential Galois theory in positive characteristic.

Contribution

It establishes the existence of proper solutions for all iterative differential embedding problems in specified algebraic function fields, filling a key gap in positive characteristic differential Galois theory.

Findings

Every iterative differential embedding problem has a proper solution.

The result applies to algebraic function fields with algebraically closed constants.

Advances the theory of differential equations in positive characteristic.

Abstract

In this paper, we prove that every iterative differential embedding problem over an algebraic function field in positive characteristic with an algebraically closed field of constants has a proper solution.