Alexander Schmidt:

Tame coverings of arithmetic schemes

       Author: Alexander Schmidt
       Title: Tame coverings of arithmetic schemes
       Year: 2000/2001
       In: Math. Annalen 322 (2002) 1--18

         Preprint (ver. April 11, 2001)   dvi   pdf   

      Abstract: We extend the notion of a tame covering of a pair (X,D) where X is a regular scheme and D is a normal crossing divisor (cf. SGA1), to pairs (X,Y) where X is an arbitrary scheme and Y is a closed subset in X. We show that the abelianized tame fundamental group of a regular scheme which is flat and of finite type over Spec(Z) is finite and does not depend on the choice of a particular compactification.