Ketu and the second invariant of a quadratic space
type: Item
instance of: scholarly article
title: Ketu and the second invariant of a quadratic space
zbMATH Open document ID: 0802.19004
DOI: 10.1007/BF00961215
author: R. Sridharan
author: Manuel Ojanguren
author: R. Parimala
published in: \(K\)-Theory
publication date: 1994-12-15T00:00:00Z
review text: Let \(A\) be a commutative ring, in which 2 is invertible, and let \(W(A)\) denote the Witt ring of \(A\) with fundamental ideal \(I(A)\). The Milnor \(K\)-group \(K_ 2(A)\) carries a natural involution \(\alpha\to \alpha^ t\) induced from the involution on the Steinberg group \(St(A)\), which interchanges the indices of the generators. \textit{C. H. Giffen} [J. Algebra 44, 434-456 (1977; Zbl 0354.16012)], defined an invariant \(c_ 2: I^ 2(A)\to K_ 2(A)/ \text{Tr}(K_ 2 (A))\) where \(\text{Tr}\colon K_ 2(A)\to K_ 2(A)\) sends \(\alpha\) to \(\alpha- \alpha^ t\). The authors show that the Giffen-invariant is related to the Clifford- invariant \(Cliff: I^ 2(A)\to H^ 2_{\text{ét}} (\text{Spec } A, \mu_ 2^{\otimes_ 2})\) via the Chern-class map \(c_{22} \colon K_ 2(A)\to H^ 2_{\text{ét}} (\text{Spec } A, \mu_ 2^{\otimes_ 2})\) defined by Soulé and Shekhtman.
Mathematics Subject Classification ID: 19G12
Mathematics Subject Classification ID: 11E81
Mathematics Subject Classification ID: 11E70
Mathematics Subject Classification ID: 19C99
Mathematics Subject Classification ID: 19F27
zbMATH DE Number: 549705
zbMATH Keywords: Chern classes
zbMATH Keywords: quadratic forms
zbMATH Keywords: Clifford invariant
zbMATH Keywords: Giffen invariant
reviewed by: Manfred Kolster
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00961215
OpenAlex ID: W2024976800
description: scientific article; zbMATH DE number 549705