On fields of \(u\)-invariant 4
type: Item
instance of: scholarly article
title: On fields of \(u\)-invariant 4
zbMATH Open document ID: 1093.11023
author: Karim Johannes Becher
published in: Archiv der Mathematik
publication date: 2006-03-21T00:00:00Z
review text: The main result of this paper is as follows: Theorem 3.1 Assume that \(u(F(\sqrt {-1}))=4\). A necessary and sufficient condition to have that \(u(F)\leq 4\) is that, for any \(a\in D_F(3)\) and \(d\in D_F(2)\), the form \(\langle 1,1,-a,-ad\rangle\) is universal over \(F\). This strengthens and generalizes an old result of the reviewer (from the year 1981). The proof is short and elementary modulo standard theorems on quadratic forms over fields. Some related results are also proved. But the main conjecture remains still open: Is it true that \(u(F)\leq 4\) for any field \(F\) of transcendence degree 2 over \(\mathbb{R}\)?
reviewed by: Albrecht Pfister
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 11E81
zbMATH DE Number: 5013995
MaRDI profile type: Publication
full work available at URL: s00013-005-1491-y
OpenAlex ID: W2007622440
DOI: 10.1007/S00013-005-1491-Y
description: scientific article; zbMATH DE number 5013995