Local-global principles for Witt rings
type: Item
instance of: scholarly article
title: Local-global principles for Witt rings
zbMATH Open document ID: 0790.11033
DOI: 10.1016/0022-4049(93)90127-F
author: Ido Efrat
published in: Journal of Pure and Applied Algebra
publication date: 1994-07-04T00:00:00Z
review text: For a collection \({\mathbf K}\) of algebraic extensions of a field \(K\) there is the natural homomorphism of the Witt ring \(W(K)\) into the sheaf product of the Witt rings of fields in \({\mathbf K}\). Conditions are studied under which the homomorphism turns out to be surjective or bijective. If the fields in \({\mathbf K}\) are contained in the quadratic closure of \(K\) and if the collection \({\mathbf K}\) is closed in a certain sense, then the natural homomorphism is an isomorphism if and only if the Galois group of the quadratic closure of \(K\) over \(K\) is a free pro-2 product of the Galois groups of the quadratic closure of \(K\) over the fields in the collection \({\mathbf K}\). This is applied to a computation of the Witt rings of real-projective fields.
Mathematics Subject Classification ID: 11E81
Mathematics Subject Classification ID: 12G05
zbMATH DE Number: 500591
zbMATH Keywords: pro-\(p\) product
zbMATH Keywords: computation of Witt rings of real-projective fields
zbMATH Keywords: Witt ring
zbMATH Keywords: sheaf product
zbMATH Keywords: homomorphisms
reviewed by: Kazimierz Szymiczek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 500591