Abstract:Using the Rost invariant for torsors under Spin groups one may define an analogue of the Arason invariant for certain hermitian forms and orthogonal involutions. We calculate this invariant explicitly in various cases, and use it to associate to every orthogonal involution σ with trivial discriminant and trivial Clifford invariant over a central simple algebra A of even co-index an element f 3 (σ) in the subgroup; it vanishes when deg A ≤ 10 and also when there is a quadratic extension of F that simultaneously… Show more
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