Solutions to arithmetic differential equations in algebraically closed fields

TL;DR

This paper demonstrates that key algebraic differential equations exhibit a total differential overconvergence property, enabling solutions to be considered within algebraically closed fields, thus broadening the scope of their applicability.

Contribution

It introduces the total differential overconvergence property for algebraic differential equations, facilitating solutions in algebraically closed fields, which was not previously established.

Findings

Key examples possess total differential overconvergence

Solutions can be considered in algebraically closed fields

Broadens applicability of algebraic differential equations

Abstract

We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solutions to these equations with coordinates in algebraically closed fields.