Foliations and Galois Theory in Positive Characteristic

TL;DR

This paper establishes a Galois-type correspondence linking purely inseparable field extensions with subalgebras of differential operators, advancing the understanding of foliation theory in positive characteristic algebraic geometry.

Contribution

It introduces a novel Galois correspondence for purely inseparable extensions and connects it to foliation theory on varieties in positive characteristic.

Findings

Established a Galois-type correspondence for purely inseparable extensions

Connected separable and purely inseparable extensions through this framework

Provided insights into foliation theory in positive characteristic

Abstract

We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between separable field extensions and purely inseparable field extensions. Specifically, it serves as a progression towards gaining a deeper comprehension of a foliation theory on varieties in positive characteristic.