Filtrations of modules, the Chow group, and the Grothendieck group
type: Item
instance of: scholarly article
title: Filtrations of modules, the Chow group, and the Grothendieck group
zbMATH Open document ID: 0949.13008
author: C-Y. Jean Chan
published in: Journal of Algebra
publication date: 1999-12-20T00:00:00Z
review text: In this paper the author proves that a finitely generated module over a Noetherian ring defines a unique cycle class in the components with codimension zero and one of the Chow group of the ring. This is an interesting result. It generalizes a classical result over integrally closed domains and implies the isomorphism between the Chow group and the Grothendieck group \((K_0\)-group) under certain conditions. In addition, the author also discusses the difference between the map constructed in this paper and the Riemann-Roch map.
reviewed by: Tong Wenting
Mathematics Subject Classification ID: 13D15
Mathematics Subject Classification ID: 14C15
Mathematics Subject Classification ID: 19A49
zbMATH DE Number: 1348099
zbMATH Keywords: filtration of a module
zbMATH Keywords: finitely generated module
zbMATH Keywords: cycle class
zbMATH Keywords: Chow group
zbMATH Keywords: Grothendieck group
zbMATH Keywords: Riemann-Roch map
MaRDI profile type: Publication
OpenAlex ID: W2123730847
cites work: Q4342000
cites work: Q4143433
cites work: A remark on the Riemann-Roch formula on affine schemes associated with Noetherian local rings
cites work: Q3739243
cites work: Q4215795
DOI: 10.1006/JABR.1999.7888
description: scientific article; zbMATH DE number 1348099