Isotropy of symplectic and unitary involutions: Appendix to a paper of N. Karpenko

Tignol, Jean-Pierre
(2013) American Journal of Mathematics — Vol. 135, n° 1, p. 12-15 (2013)

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Abstract
A symplectic involution on a central simple algebra that becomes isotropic over every scalar extension where the algebra has index 2 becomes isotropic over some odd-degree extension. Likewise, a unitary involution on a central simple algebra of exponent 2 that becomes isotropic over every field extension where the algebra is split also becomes isotropic over an odd-degree field extension.
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Tignol, J.-P. (2013). Isotropy of symplectic and unitary involutions: Appendix to a paper of N. Karpenko. American Journal of Mathematics, 135(1), 12-15. https://doi.org/10.1353/ajm.2013.0011 (Original work published 2013)