The minimal height of quadratic forms of given dimension
type: Item
instance of: scholarly article
title: The minimal height of quadratic forms of given dimension
zbMATH Open document ID: 1109.11023
author: Nikita Karpenko
author: Ulf Rehmann
author: Jurgen Hurrelbrink
published in: Archiv der Mathematik
publication date: 2007-02-14T00:00:00Z
review text: The height \(h(\phi)\) of an anisotropic quadratic form over a field is the length of the splitting tower of \(\phi\). \textit{J. Hurrelbrink} and \textit{U. Rehmann} [J. Reine Angew. Math. 444, 183--192 (1993; Zbl 0791.11016)] determined the height of an excellent form of dimension \(n\) from the representation of \(n\) in the form of alternating sum of distinct \(2-\)powers. They conjectured that the height of anisotropic excellent form of dimension \(n\) is minimal among the heights of all anisotropic forms of dimension \(n\). In the present paper this conjecture is proved by using an improved version of the results of \textit{N. A. Karpenko} [Invent. Math. 153, No.~2, 455--462 (2003; Zbl 1032.11016)].
reviewed by: Kazimierz Szymiczek
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 14C25
zbMATH DE Number: 5126583
zbMATH Keywords: Excellent quadratic forms
zbMATH Keywords: splitting pattern of anisotropic quadratic forms
MaRDI profile type: Publication
full work available at URL: s00013-006-1833-4
OpenAlex ID: W2120921856
DOI: 10.1007/S00013-006-1833-4
description: scientific article; zbMATH DE number 5126583