Abstract
Let X be a regular arithmetic scheme, i.e. a regular integral separated scheme flat and of finite type over Spec Z . Assume that for all closed irreducible subschemes C ⊆ X of dimension 1 with normalisation C ˜ there are given open normal subgroups N C of π 1 ( C ˜ ) , which fulfil the following compatibility condition: For all x ˜ ∈ C ˜ 1 × X C ˜ 2 the pre-images of N C 1 and N C 2 in π 1 ( x ˜ ) coincide. If the indices of the N C are bounded, then these data uniquely determine an open normal subgroup of π 1 ( X ) , whose pre-image in π 1 ( C ˜ ) is N C for all C.
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