Factoring differential operators over algebraic curves in positive characteristic

Raphaël Pagès (1, 2, 3)

1 IMB - Institut de Mathématiques de Bordeaux
2 UB - Université de Bordeaux
3 MATHEXP - Calcul formel, mathématiques expérimentales et interactions

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.

Domaines: Algèbres d'opérateurs [math.OA]; Calcul formel [cs.SC]

Raphaël Pagès. Factoring differential operators over algebraic curves in positive characteristic. ISSAC 2022 - International Symposium on Symbolic and Algebraic Computation, Jul 2022, Lille, France. ⟨hal-03759105⟩