✦ LIBER ✦

A construction of covers of arithmetic schemes

✍ Scribed by Götz Wiesend

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 175 KB
Volume: 121
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.01.006

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✦ Synopsis

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 ∈ C1 × X C2 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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