Foliations and Galois Theory in Positive Characteristic

Author:

Przemyslaw Grabowski

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Commutative Algebra (math.AC), Rings and Algebras (math.RA)

journal:

date:

2023-07-20 16:00:00

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.

PDF: Foliations and Galois Theory in Positive Characteristic.pdf