Kolchin's irreducibility theorem. (Q2487997)

The authors present a very interesting link between Kolchin's theory of differential ideals and the theory of arcs traced on an algebraic variety initiated by J. F. Nash. As a main result they prove a version of the Kolchin irreducibility theorem in terms of schemes of arcs in characteristic zero. In positive characteristic they give a simple counter-example in the case of surfaces.