Le principe de scindage et l'inexistence d'une \(K\)-théorie de Milnor globale. (The splitting principle and the non-existence of global Milnor \(K\)-theory)
type: Item
instance of: scholarly article
title: Le principe de scindage et l'inexistence d'une \(K\)-théorie de Milnor globale. (The splitting principle and the non-existence of global Milnor \(K\)-theory)
zbMATH Open document ID: 0768.55003
DOI: 10.1016/0040-9383(92)90052-J
published in: Topology
publication date: 1993-05-16T00:00:00Z
review text: The main result of this paper is a minimality result for the Quillen \(K\)- theory of smooth quasi-projective schemes over a field \(k\). Let \(F\) be a functor on such schemes which satisfies some natural axioms; in particular there is to be a natural transformation \(\eta:F\to K\), where \(K\) is the Quillen \(K\)-theory. The author shows that \(\eta:F_ *(X)\to K_ *(X)\) is surjective for each \(X\). As a consequence, there is no good extension of the Milnor \(K\)-theory \(K_ *^ M(k)\) to the category of schemes.
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 19D45
zbMATH DE Number: 166192
zbMATH Keywords: Quillen \(K\)-theory of smooth quasi-projective schemes
zbMATH Keywords: Milnor \(K\)-theory
author: Robert W. Thomason
reviewed by: Richard John Steiner
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 166192