S. Garibaldi, R. Parimala, J.-P. Tignol: Discriminant of symplectic involutions

skip@member.ams.org, parimala@mathcs.emory.edu, jean-pierre.tignol@uclouvain.be

Submission: 2007, Jul 13

We define an invariant of torsors under adjoint linear algebraic groups of type C_n --- equivalently, central simple algebras of degree 2n with symplectic involution --- for n divisible by 4 that takes values in H^3(k,2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple algebra of degree 8 with symplectic involution can be decomposed as a tensor product of quaternion algebras with involution.

2000 Mathematics Subject Classification: 16W10, 11E72

Keywords and Phrases: cohomological invariant, symplectic group

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