Étale Covers and Fundamental Groups of Schematic Finite Spaces

Abstract We introduce the category of finite étale covers an arbitrary schematic space X and show that, equipped with appropriate natural fiber functor, it is a Galois Category. This allows us to define fundamental group spaces. If model scheme S , we that resulting theory on coincides classical therefore, recover introduced by Grothendieck. To prove these results, crucial find suitable geometric notion connectedness for spaces also study their points. achieve goals means strong cohomological constraints enjoyed