Karpenko's anisotropy conjecture for orthogonal involutions

Let AA be a central simple algebra over a field FF, and let FA,o{\mathcal F}_{A,o} denote the function field associated with AA and orthogonal involutions. An orthogonal involution on AA is anisotropic if it has no nonzero isotropic elements. Karpenko's anisotropy conjecture. An anisotropic orthogonal involution remains anisotropic over FA,o{\mathcal F}_{A,o}. This conjecture asks whether anisotropy of orthogonal involutions is preserved under passage to the generic function field associated with orthogonal involutions. The supplied text does not state whether the conjecture has been resolved.

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Primary source

Jodi Black and Anne Quéguiner-Mathieu, “Involutions, odd-degree extensions and generic splitting”, arXiv:1310.1505 (2014).

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