Differential Galois theory in positive characteristic

Speaker: Mathieu Florence, Paris 6

Abstract: Let k be a field of characteristic p>0, equipped with a derivation d; that is, an additive map from k to itself satisfying the Leibnitz rule. Let C be the field of constants of d; we assume that the extension k/C is finite. The main result of this talk is an equivalence between the category of differential modules for (k,d) and that of modules over an Azumaya algebra over the ring C[X], of which we give a concrete description. As an application, we give a necessary and sufficient condition for a differential module (or equation) to be cyclic.