Vol. 293, No. 2, 2018

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ISSN: 0030-8730
Group and round quadratic forms

James O’Shea

Vol. 293 (2018), No. 2, 391–405
DOI: 10.2140/pjm.2018.293.391
Abstract

We offer some elementary characterisations of group and round quadratic forms. These characterisations are applied to establish new (and recover existing) characterisations of Pfister forms. We establish “going-up” results for group and anisotropic round forms with respect to iterated Laurent series field extensions, which contrast with the established results with respect to rational function field extensions. For forms of two-power dimension, we determine when there exists a field extension over which the form becomes an anisotropic group form that is not round.

Keywords
quadratic forms, round forms, group forms, Pfister forms
Mathematical Subject Classification 2010
Primary: 11E04, 11E10, 11E81, 11E99, 12F20
Milestones
Received: 8 June 2017
Revised: 23 July 2017
Accepted: 9 August 2017
Published: 23 November 2017
Authors
James O’Shea
Department of Mathematics and Statistics
National University of Ireland, Maynooth
Ireland