A K-theoretic approach to multiplicities
type: Item
instance of: scholarly article
title: A K-theoretic approach to multiplicities
zbMATH Open document ID: 0546.13014
DOI: 10.1007/BF01456079
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163979
review text: We examine the relationship between Gersten's conjecture on a regular local ring R, and the structure of the group \(K_ 0(M_ R^{(i)})\), where \(M_ R^{(i)}\) is the category of finitely generated R modules supported in codimension at least i. We show that, for R of the form \(\Lambda x_ 1,...,x_ n/\sum^{k}_{i=1}x^ 2_ i-p,\) with \(\Lambda\) a DVR with maximal ideal (p), \(K_ 0(M_ R^{(i)})\) is generated by cyclic modules of the form \(R/(f_ 1,...,f_ i)\), where \((f_ 1,...,f_ i)\) is a regular sequence. As an application, this proves the vanishing part of Serre's multiplicity conjecture for rings with completion isomorphic to R.
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 13D15
Mathematics Subject Classification ID: 13H05
zbMATH DE Number: 3869489
zbMATH Keywords: K-theory
zbMATH Keywords: regular local ring
zbMATH Keywords: regular sequence
zbMATH Keywords: multiplicity conjecture
author: Marc Levine
MaRDI profile type: Publication
cites work: Generalized Intersection Multiplicities of Modules
cites work: Weak linking and multiplicities
cites work: The relative form of Gersten's conjecture over a discrete valuation ring: The smooth case
OpenAlex ID: W2055981044
description: scientific article; zbMATH DE number 3869489