Some results on the lower K-theory of singular affine varieties
type: Item
instance of: scholarly article
title: Some results on the lower K-theory of singular affine varieties
zbMATH Open document ID: 0617.14007
DOI: 10.1016/0022-4049(86)90079-4
author: Les Reid
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: The author gives sufficient conditions for the construction of nonzero elements of the lower algebraic K-theory, \(N^ iK_{-j}(A)\) where A is a singular coordinate ring. For low values of j this sort of calculation has been made in many cases by means of the conductor/normalisation Cartesian square of J. Milnor and its attendant exact sequence. When A is higher-dimensional this method will not work since normalisations need not be regular (A might be its own normalisation). The author circumvents these difficulties by introducing suitable rings which, while not geometric in origin, have Mayer-Vietoris sequences and computable lower K-groups. He then lifts some of the elements which he obtains in this manner.
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 4000094
zbMATH Keywords: nonzero elements of the lower algebraic K-theory
zbMATH Keywords: singular coordinate ring
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90079-4
OpenAlex ID: W1971668628
cites work: Q5562621
cites work: Q4085905
cites work: Q3240881
cites work: Relative K-theory and vector bundles on certain singular varieties
cites work: Generators and relations of abelian semigroups and semigroup rings
cites work: Q5611879
cites work: Introduction to Algebraic K-Theory. (AM-72)
cites work: Q4769130
cites work: K-theory and analytic isomorphisms
description: scientific article; zbMATH DE number 4000094