Titre : Fundamental group schemes and differential equations in positive characteristic.

Résumé :

Since Riemann we know that differential equations and topology are related. The (not very) modern conception of this relation asserts that there is an equivalence between integrable connections and representations of the fundamental group. In this seminar we discuss what can be done in positive characteristic. Integrable connections are replaced by D-modules (D= diff. ops of EGA IV) and the fundamental group is replaced by the group scheme of Saavedra (all is developed without leaving positive characteristic.)
We will show some properties of this group: it is a perfect scheme in general and, for a proper ambient variety, the largest unipotent quotient is pro-etale. A computation for abelian varieties will be exhibited. If time allows, we will discuss the failures of the naïve analogy in the rigid analytic setting.

<Retour>