Weigth zero motivic cohomology and the general linear group of a simplicial ring
type: Item
instance of: scholarly article
title: Weigth zero motivic cohomology and the general linear group of a simplicial ring
zbMATH Open document ID: 0945.19001
DOI: 10.1016/S0022-4049(98)00141-8
author: Mark E. Walker
published in: Journal of Pure and Applied Algebra
publication date: 2000-09-27T00:00:00Z
review text: The author compares the weight zero parts of two filtrations on the K-theory of a regular ring \(R\) all of whose residue fields are infinite. Both filtrations have been conjectured to lead to a motivic Atyah-Hirzebruch spectral sequence. The first filtration is called \(C^\bullet\) and was introduced in [\textit{S. E. Landsburg}, K-Theory 6, No. 5, 431-455 (1992; Zbl 0774.14006)]. The other filtration is called \(W^\bullet\) and was originally suggested by Goodwillie and Lichtenbaum. The point of this paper is to show that the weight zero parts agree. This also corrects a mistake in Landsburg's paper and shows that the \(C^\bullet\) filtration is actually better behaved than that paper indicates. In the computations the author exploits that one meets simplicial rings that satisfy the `primitive criterion' introduced by the reviewer [\textit{W. van der Kallen}, Ann. Sci. Éc. Norm. Supér., IV. Ser. 10, 473-515 (1977; Zbl 0393.18012)]. Recall that this criterion guarantees there are plenty of units.
Mathematics Subject Classification ID: 19E08
Mathematics Subject Classification ID: 14F42
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 19E15
Mathematics Subject Classification ID: 14C25
zbMATH DE Number: 1435992
zbMATH Keywords: primitive criterion
zbMATH Keywords: motivic cohomology
zbMATH Keywords: filtration on K-theory of regular ring
reviewed by: Wilberd van der Kallen
MaRDI profile type: Publication
full work available at URL: s0022-4049(98)00141-8
OpenAlex ID: W2068194863
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description: scientific article; zbMATH DE number 1435992