Class groups and Picard groups of normal schemes
type: Item
instance of: scholarly article
title: Class groups and Picard groups of normal schemes
zbMATH Open document ID: 0568.14006
DOI: 10.1016/0022-4049(85)90095-7
author: Steven E. Landsburg
published in: Journal of Pure and Applied Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let \(\phi\) : \(X\to Y\) be a dominant morphism of irreducible noetherian schemes with Y reduced and normal. Let \(T=\phi^{-1}(Sing(Y))\). Assume that T has codimension \(\geq 2\) in X and contains Sing(X) and that \(\phi\) \(| T: T\to Sing(Y)\) is an isomorphism. Under these conditions it is proved that the map \(\ker (Pic(Y)\to Pic(X))\to \ker (Cl(Y)\to Cl(X))\) is an isomorphism. Some standard results on the relation between the divisor class groups of a normal domain A and those of certain localizations (resp. completions) of A are obtained as immediate corollaries.
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 14E05
zbMATH DE Number: 3906620
zbMATH Keywords: Picard groups
zbMATH Keywords: dominant morphism
zbMATH Keywords: divisor class groups
reviewed by: Balwant Singh
MaRDI profile type: Publication
full work available at URL: 0022-4049(85)90095-7
OpenAlex ID: W2035508736
cites work: Patching theorems for projective modules
cites work: The Milnor patching property
description: scientific article; zbMATH DE number 3906620