Factoring differential operators over algebraic curves in positive characteristic

TL;DR

This paper introduces an algorithm for factoring linear differential operators over algebraic curves in positive characteristic, utilizing tools like p-curvature and p-Riccati equations unique to this setting.

Contribution

It presents a novel algorithm that leverages positive characteristic tools to factor differential operators over algebraic curves.

Findings

Algorithm successfully factors differential operators in positive characteristic

Utilizes p-curvature and p-Riccati equations for factorization

Advances understanding of differential operators in algebraic geometry

Abstract

We present an algorithm for factoring linear differential operators with coefficients in a finite separable extension of F p (x). Our methods rely on specific tools arising in positive characteristic: p-curvature, structure of simple central algebras and p-Riccati equations.