A method for computing the kernel of a map of divisor classes of local rings in characteristic p\(\neq 0\)
type: Item
instance of: scholarly article
title: A method for computing the kernel of a map of divisor classes of local rings in characteristic p\(\neq 0\)
zbMATH Open document ID: 0655.13023
published in: Michigan Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let k be an algebraically closed field of characteristic \(p=0\) and \(G\in k[X,Y]\) be an polynomial, m a natural number and \(X_ m\) the surface in \({\mathbb{A}}\) \(3_ k\) defined by \(z^{p\quad m}-G=0\). The purpose of this paper is to study the divisor class group \(Cl(X_ m)\) of \(X_ m\). The idea is to define a morphisms \(\phi_ m:\quad C1(X_{m+1})\to C1(X_ m)\) and obtain information on \(C1(X_{m+1})\) from \(C1(X_ m)\). You can find some explicit examples. It should be said that \textit{P. Samuel} calculated some examples in his book ``Lectures on unique factorization domains'' (Tata Inst. Fund. Res., Bombay 1964; Zbl 0184.066)].
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14J25
zbMATH DE Number: 4069049
zbMATH Keywords: divisor class group of affine surface
author: Jeffrey Lang
author: Piotre Blass
reviewed by: Marcel Morales
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003682
OpenAlex ID: W2024009538
DOI: 10.1307/MMJ/1029003682
description: scientific article; zbMATH DE number 4069049