English

Group and round quadratic forms

Number Theory 2018-03-16 v1

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 fields, 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

Cite

@article{arxiv.1705.04360,
  title  = {Group and round quadratic forms},
  author = {James O'Shea},
  journal= {arXiv preprint arXiv:1705.04360},
  year   = {2018}
}

Comments

12 pages

R2 v1 2026-06-22T19:44:36.326Z