Karpenko's anisotropy conjecture for orthogonal involutions
Karpenko's anisotropy conjecture for orthogonal involutions
Let be a central simple algebra over a field , and let denote the function field associated with and orthogonal involutions. An orthogonal involution on is anisotropic if it has no nonzero isotropic elements. Karpenko's anisotropy conjecture. An anisotropic orthogonal involution remains anisotropic over . 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.
Sources & referencesView supporting material
Primary source
Jodi Black and Anne Quéguiner-Mathieu, “Involutions, odd-degree extensions and generic splitting”, arXiv:1310.1505 (2014).
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