Over the complex numbers, the étale fundamental group controls (regular singular if the manifold is not proper) O-coherent D- modules, called stratifications, or crystals. We discuss the characteristic $p$ analogs, the Gieseker conjecture for stratifications, the de Jong conjecture for crystals. We proved the Gieseker conjecture in the proper case ( with Mehta). We will discuss some points of the proof, and for the other open cases we will present the last progresses.