On centralizers in Azumaya domains

TL;DR

This paper proves a positive characteristic analogue of a classical result about the commutativity of centralizers of differential operators, providing a new proof of the characteristic zero case via reduction modulo p.

Contribution

It introduces a positive characteristic analogue of a classical theorem and offers a novel proof of the characteristic zero result through reduction modulo p.

Findings

Centralizer of a nonconstant differential operator in positive characteristic is commutative.

New proof of the classical characteristic zero result via reduction modulo p.

Simplifies understanding of differential operators in algebraic geometry.

Abstract

We prove a positive characteristic analogue of the classical result that the centralizer of a nonconstant differential operator in one variable is commutative. This leads to a new, short proof of that classical characteristic zero result, by reduction modulo $p.$