Étale fundamental groups and stratifications

Over the field of complex numbers, the étale fundamental group controls the local systems, or equivalently the regular singular flat connections, as the topological fundamental group is finitely generated (Malčev-Grothendieck). We describe analogies in characteristic $p>0$, for stratifications (or equivalently $\mathbb{O}$-coherent $\mathbb{D}$-modules, or equivalently Frobenius divided sheaves, or equivalently crystals in the infinite site). In particular, we list some non-trivial examples of smooth non-proper varieties which are simply connected in characteristic $p>0$.