G. Berhuy, M. Monsurro, J.-P. Tignol: The discriminant of a symplectic involution

gregory.berhuy@epfl.ch, monsurro@masg1.epfl.ch, tignol@math.ucl.ac.be

Submission: 2002, Mar 15

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 with symplectic involution.

2000 Mathematics Subject Classification: 11E72

Keywords and Phrases: central simple algebras with involution, trace forms

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