Vanishing of Euler class groups
type: Item
instance of: scholarly article
title: Vanishing of Euler class groups
zbMATH Open document ID: 1117.13008
author: Ken Parker
author: Satyagopal Mandal
published in: Journal of Algebra
publication date: 2007-02-26T00:00:00Z
review text: Let \(A\) be a noetherian ring and and \(L\) a rank one projective \(A\)-module, and let \(E(A,L)\) denote the Euler class group. This paper contains several results about the vanishing of \(E(A,L)\). One of the main results is as follows. Let \(f\in A[X]\) be a non-zero divisor, and let \(B=A[X,1/f]\), with \(\dim(B)=\dim(A)+1=n\). If \(L\) is a line bundle over \(\text{Spec}(B)\), then the Euler class group \(E(B,L)=0\).
reviewed by: Reinhard Laubenbacher
Mathematics Subject Classification ID: 13C10
zbMATH DE Number: 5129709
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.06.012
OpenAlex ID: W2088701607
cites work: Q4504511
cites work: Zero cycles and the Euler class groups of smooth real affine varieties
cites work: A Riemann-Roch theorem
cites work: Euler class construction
cites work: Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
cites work: Q5288190
cites work: Projective modules and complete intersections
cites work: Stability theorems for overrings of polynomial rings. II
cites work: An Elementary Transformation of a Special Unimodular Vector to Its Top Coefficient Vector
cites work: The Conjectures of Eisenbud and Evans
cites work: Projective modules over polynomial rings
DOI: 10.1016/J.JALGEBRA.2006.06.012
description: scientific article; zbMATH DE number 5129709