On quadratic forms and Galois cohomology
type: Item
instance of: scholarly article
title: On quadratic forms and Galois cohomology
zbMATH Open document ID: 0703.11021
DOI: 10.1216/RMJ-1989-19-3-575
author: Jón Kr. Arason
author: Richard Elman
author: Bill Jacob
published in: Rocky Mountain Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: This is a survey article concerning the ``Milnor problems'' on the isomorphism of the groups \(\bar I^ nF=I^ nF/I^{n-1}F,\quad H^ nF,\quad H^ n_ qF,\quad k_ nF\) for all fields F and all \(n\in {\mathbb{N}}_ 0\). It was presented at the 1986 Corvallis Conference on Quadratic Forms and Real Algebraic Geometry. In the meantime considerable progress has been achieved by \textit{B. Jacob} and \textit{M. Rost} [Invent. Math. 96, 551-570 (1989; Zbl 0685.10015)] and, independently, by Merkur'ev-Suslin: For \(n\leq 3\) these groups are all isomorphic, for \(n=4\) the homomorphism \(e^ 4_ F: \bar I^ 4F\to H^ 4F\) exists.
Mathematics Subject Classification ID: 11E81
Mathematics Subject Classification ID: 12G05
zbMATH DE Number: 4152468
zbMATH Keywords: Galois cohomology
zbMATH Keywords: Witt ring
zbMATH Keywords: survey
zbMATH Keywords: Milnor problems
zbMATH Keywords: homomorphism
reviewed by: Albrecht Pfister
MaRDI profile type: Publication
full work available at URL: rmj-1989-19-3-575
OpenAlex ID: W1985245164
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description: scientific article; zbMATH DE number 4152468