Symplectic Involutions, quadratic pairs and function fields of conics

TL;DR

This paper classifies symplectic involutions and quadratic pairs that become hyperbolic over conic function fields, extending known results to arbitrary fields and deriving implications for minimal quadratic forms.

Contribution

It provides a classification of degree 4 symplectic involutions and quadratic pairs over arbitrary fields, generalizing previous characteristic-dependent results.

Findings

Classification of symplectic involutions in degree 4

Results on 5-dimensional minimal quadratic forms

Extension of known results to characteristic 2 fields

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.