Symplectic Involutions, quadratic pairs and function fields of conics

2016/04/16 by Dolphin, Andrew, Quéguiner-Mathieu, Anne
#11E39 #11E81 #12F05 #12F10 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1604.04733

Abstract

In this paper we study symplectic involutions and quadratic pairs that become hyperbolic over the function field of a conic. In particular, we classify them in degree 4 and deduce results on 5 dimensional minimal quadratic forms, thus extending to arbitrary fields some results of [24], which were only known in characteristic different from 2.

Related

• Algebras with involution that become hyperbolic over the fonction field of a conic
• Hyperbolicity over function fields of quadrics
• Minimal quadratic forms for the function field of a conic in characteristic 2
• 5-dimensional minimal quadratic and bilinear forms over function fields of conics
• Involutions, odd-degree extensions and generic splitting