Fields of characteristic 2 with prescribed u-invariants
type: Item
instance of: scholarly article
title: Fields of characteristic 2 with prescribed u-invariants
zbMATH Open document ID: 0713.12002
DOI: 10.1007/BF01459240
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164813
review text: For a field F of characteristic 2, the following invariants are considered: \[ u(F)=\sup \{\dim q|\;q\text{ anisotropic nonsingular quadratic form over }F\} \] \[ \hat u(F)=\sup \{\dim q|\;q\text{ anisotropic quadratic form over }F.\}. \] The methods Merkurjev used to construct fields of characteristic not 2 with arbitrary even u-invariant are adapted to the characteristic 2 case in the present paper, and are used to construct the following kind of examples in characteristic 2: 1) a field F with \(u(F)=\hat u(F)=6\). 2) for any integers n,m such that \(2^ m\geq 2n\geq 4\) and \(m\geq n-1\), a field F with \(u(F)=2n\) and \(\hat u(F)=2^ m\). 3) for any integer \(n\geq 2\), a field F with \(u(F)=2n\) and \(\hat u(F)=\infty\).
Mathematics Subject Classification ID: 12E99
Mathematics Subject Classification ID: 11E04
zbMATH DE Number: 4173145
zbMATH Keywords: field of characteristic 2
zbMATH Keywords: u-invariant
author: Pasquale Mammone
author: Jean-Pierre Tignol
author: A. R. Wadsworth
reviewed by: Jean-Pierre Tignol
MaRDI profile type: Publication
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OpenAlex ID: W1979071986
description: scientific article; zbMATH DE number 4173145