Scaled trace forms over number fields
type: Item
instance of: scholarly article
title: Scaled trace forms over number fields
zbMATH Open document ID: 0607.10013
DOI: 10.1007/BF01191998
author: William C. Waterhouse
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: Let k be a field of characteristic \(\neq 2\), a scaled trace form is a quadratic form \(Q(x)=tr_{L/k}(bx^ 2)\), where L/k is a finite separable extension and \(b\in L^{\times}\). The author proves that every nondegenerate quadratic form over a hilbertian field is isometric to a scaled trace form. The proof uses a matrix characterization of scaled trace forms and Hilbert's irreducibility theorem.
Mathematics Subject Classification ID: 11E12
Mathematics Subject Classification ID: 12F99
zbMATH DE Number: 3981256
zbMATH Keywords: scaled trace form
zbMATH Keywords: quadratic form
zbMATH Keywords: hilbertian field
reviewed by: Nuria Vila
MaRDI profile type: Publication
cites work: Q3344268
cites work: Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants.
cites work: The Witt invariant of the form \(\text{Tr}(x^ 2)\)
cites work: On the similarity transformation between an integral matrix with irreducible characteristic polynomial and its transpose
cites work: Pairs of quadratic forms
full work available at URL: https://doi.org/10.1007/bf01191998
OpenAlex ID: W1983398641
description: scientific article; zbMATH DE number 3981256