Andrew Dolphin and Anne Quéguiner-Mathieu: Symplectic Involutions, quadratic pairs and function fields of conics,

Submission: 2016, Jan 8

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.

2010 Mathematics Subject Classification: 11E39, 11E81, 12F05, 12F10.

Keywords and Phrases: Central simple algebras, involutions, characteristic two, quadratic forms, quadratic pairs, conics.

Full text: dvi.gz 40 k, dvi 99 k, ps.gz 809 k, pdf.gz 199 k, pdf 220 k.

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