Etale coverings of formal schemes

Stale schemes in general we shall see that 3.2.2 is a special case 

3) 1) Clear because only condition 3) of 3.2.2 remains to be checked, but the closed fibres are the same for Spec A and Spf A. 

Let RevEt( /) denote the full subcategory of formal cf -schemes, for which f is an Stale covering (cf.also 2.4-.1 ). Put for every integer n o 

Corollary 3.2.5. Let X be connected. Then RevEtC ) is a Galois category. 

Prooft We have to make a fibre functor. Take s f andJX a separably closed field containing k(s).Then we have a geometric point 

If f X — S is a finite morphism of usual schemes then the set of points s6S for which there exists a point xgX with f(x)= s such that f is ramified at x, is a closed set (EGA IV I7.3.7 )  

---