Let X be a normal noetherian scheme and Z ⊆ X a closed subset of codimension ≥ 2. We consider here the local obstructions to the map π̂1(X/Z) → π̂1(X) being an isomorphism. Assuming X has a regular alteration, we prove the equivalence of the obstructions being finite and the existence of a Galois quasi-étale cover of X, where the corresponding map on fundamental groups is an isomorphism.
|Published - Jul 26 2017
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