\(K_2\) of localisations of local rings
type: Item
instance of: scholarly article
title: \(K_2\) of localisations of local rings
zbMATH Open document ID: 1308.19003
published in: Journal of Algebra
publication date: 2014-08-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1205.0860
review text: Let \(A\) be a commutative local ring whose residue field has \(>5\) elements. Then it is known that the Quillen \(K\)-group \(K_2(A)\) is isomorphic to the target \(K_2^M(A)\) of the universal Steinberg symbol. This target is also known as the second Milnor \(K\)-group of \(A\). Now assume that \(A\) is also regular. Let \(t_1,\dots,t_n\) be irreducible elements in \(A\) such that the quotient of \(A\) by an ideal generated by any number of the \(t_i\) is still regular. Then the remarkable result is that \(K_2^M(A_{t_1\cdots t_n})\to K_2(A_{t_1\cdots t_n})\) is also an isomorphism.
reviewed by: Wilberd van der Kallen
Mathematics Subject Classification ID: 19C20
zbMATH DE Number: 6329088
zbMATH Keywords: algebraic \(K\)-theory
zbMATH Keywords: Steinberg symbols
zbMATH Keywords: local rings
MaRDI profile type: Publication
OpenAlex ID: W2152656764
arXiv ID: 1205.0860
cites work: Q4085905
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DOI: 10.1016/J.JALGEBRA.2013.09.026
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description: scientific article; zbMATH DE number 6329088