Five-dimensional minimal quadratic and bilinear forms over function fields of conics

Adam Chapman and Ahmed Laghribi

Vol. 339 (2025), No. 2, 243–264

DOI: 10.2140/pjm.2025.339.243

Abstract

Over a field of characteristic $2$, we give a complete classification of quadratic and bilinear forms of dimension $5$ that are minimal over the function field of an arbitrary conic. This completes the unique known case due to Faivre concerning the classification of minimal quadratic forms of dimension $5$ and type $(2,1)$ over function fields of nondegenerate conics.

Keywords

quadratic form, bilinear form, function field of a conic, minimal form, quasi-Pfister neighbor

Mathematical Subject Classification

Primary: 11E04, 11E81

Milestones

Received: 9 April 2025

Revised: 28 August 2025

Accepted: 29 August 2025

Published: 21 September 2025