The discriminant of a symplectic involution

Grégory Berhuy, Marina Monsurrò and Jean-Pierre Tignol

Vol. 209 (2003), No. 2, 201–218

DOI: 10.2140/pjm.2003.209.201

Abstract

An invariant for symplectic involutions on central simple algebras of degree divisible by 4 over fields of characteristic different from 2 is defined on the basis of Rost’s cohomological invariant of degree 3 for torsors under symplectic groups. We relate this invariant to trace forms and show how its triviality yields a decomposability criterion for algebras of degree 8 with symplectic involution.

Milestones

Received: 15 March 2002

Revised: 20 May 2002

Published: 1 April 2003