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