Appears in collection : Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday

We will consider étale coverings $ f : Y {\rightarrow} X$ of varieties over an algebraically closed field in characteristic p > 0 (with some further restrictions on the boundary ramification, in the non-proper case). This talk will give an overview of some work done with Hélène Esnault and others over the last few years, as well as open problems, related to this theme.