Factoring Partial Differential Systems in Positive Characteristic

Abstract

An algorithm for factoring differential systems in characteristic p has been given by Cluzeau in [7]. It is based on both the reduction of a matrix called p-curvature and eigenring techniques. In this paper, we generalize this algorithm to factor partial differential systems in characteristic p. We show that this factorization problem reduces effectively to the problem of simultaneous reduction of commuting matrices.In the appendix, van der Put shows how to extend his classification of differential modules, used in the work of Cluzeau, to partial differential systems in positive characteristic.