Étale fundamental group and $D$-modules in characteristic $p>0$

I will report a joint work with H. Esnault (Stratified bundles and étale fundamental group, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XIII (2014), 795-812), in which we prove the last two statements of a conjecture raised by D. Gieseker on 1975 (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2) 4 (1975), 1-31).