Abstract :
Let X be a regular arithmetic scheme, i.e. a regular integral separated scheme flat and of finite type over image. Assume that for all closed irreducible subschemes Csubset of or equal toX of dimension 1 with normalisation image there are given open normal subgroups NC of image, which fulfil the following compatibility condition: For all image the pre-images of NC1 and NC2 in image coincide. If the indices of the NC are bounded, then these data uniquely determine an open normal subgroup of π1(X), whose pre-image in image is NC for all C.
