Torsion in \(K_ 2\) of fields and 0-cycles on rational surfaces
type: Item
instance of: scholarly article
title: Torsion in \(K_ 2\) of fields and 0-cycles on rational surfaces
zbMATH Open document ID: 0574.14009
DOI: 10.1007/BF02566343
author: M. Pavaman Murthy
author: Amit Roy
published in: Commentarii Mathematici Helvetici
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/139970
review text: Let k be a field which is algebraically closed in K. Using ''Hilbert's theorem 90 for \(K_ 2''\), proved by Merkurev-Suslin, the authors show, inter alia, that \(i: K_ 2(k)\to K_ 2\)(K) is injective in characteristic zero and that ker(i) is p-primary torsion in characteristic p. Amongst the applications much of these results are some finiteness results for \(A_ 0(X)\), the group of 0-cycles of degree zero on a rational surface X over suitably nice fields (e.g. k local). Suslin has also obtained these results and similar results have been obtained by J.- L. Colliot-Thélène, W. Raskin, J.-J. Sansuc and C. Soulé [see for example \textit{J.-L. Colliot-Thélène}, \textit{J.-J. Sansuc} and \textit{C. Soulé}, C. R. Acad. Sci., Paris, Sér. I 294, 749-752 (1982; Zbl 0572.14005)].
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 3916442
zbMATH Keywords: \(K_ 2\)
zbMATH Keywords: group of 0-cycles
zbMATH Keywords: rational surface
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3916442