ÉTALE COVERS AND LOCAL ALGEBRAIC FUNDAMENTAL GROUPS

Charlie Stibitz

ÉTALE COVERS AND LOCAL ALGEBRAIC FUNDAMENTAL GROUPS

Charlie Stibitz^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Journal	Unknown Journal
State	Published - Jul 26 2017
Externally published	Yes

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Cite this

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title = "{\'E}TALE COVERS AND LOCAL ALGEBRAIC FUNDAMENTAL GROUPS",

abstract = "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 {\^π}1(X/Z) → {\^π}1(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-{\'e}tale cover of X, where the corresponding map on fundamental groups is an isomorphism.",

author = "Charlie Stibitz",

year = "2017",

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day = "26",

language = "English (US)",

journal = "Unknown Journal",

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AU - Stibitz, Charlie

PY - 2017/7/26

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N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=85093028172&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85093028172

SN - 0891-5849

JO - Unknown Journal

JF - Unknown Journal

ER -

ÉTALE COVERS AND LOCAL ALGEBRAIC FUNDAMENTAL GROUPS

Abstract

ASJC Scopus subject areas

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