Restriction of divisor classes to hypersurfaces in characteristic \(p\)
type: Item
instance of: scholarly article
title: Restriction of divisor classes to hypersurfaces in characteristic \(p\)
zbMATH Open document ID: 1056.13011
author: Phillip Griffith
author: Sandra Spiroff
published in: Journal of Algebra
publication date: 2004-10-01T00:00:00Z
review text: Let \(A\) be a Noetherian normal domain of equicharacteristic zero, and let \(f\in A\) be an element such that the ring \(A/fA\) satisfies the condition \(R_1\). \textit{S. Spriroff} defined a map \(\text{Cl}(A)\to \text{Cl}((A/fA)')\) of divisor class groups, where \((A/fA)'\) is the integral closure of \(A/fA\), and gave some conditions for injectivity [J. Pure Appl. Algebra 186, No. 1, 77--89 (2004; Zbl 1095.13009)]. In the paper under review the authors study similar questions in the case of characteristic \(p>0\). In addition, in the case when the ring \(A/fA\) is normal, they also compute quite explicitly the kernel of \(\text{Cl}(A)\to \text{Cl}(A/fA)\) and exhibit examples with non-trivial kernel.
Mathematics Subject Classification ID: 13C20
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 14J70
zbMATH DE Number: 2105398
zbMATH Keywords: divisor class group
zbMATH Keywords: hypersurfaces
zbMATH Keywords: characteristic \(p\)
reviewed by: Lucian Bădescu
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.08.002
OpenAlex ID: W2034977193
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DOI: 10.1016/J.JALGEBRA.2003.08.002
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description: scientific article; zbMATH DE number 2105398