email@example.com, firstname.lastname@example.org, email@example.com
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
Full text: dvi.gz 40 k, dvi 93 k, ps.gz 793 k, pdf.gz 207 k, pdf 233 k.