Hyperbolicity of Orthogonal Involutions

We show that a non-hyperbolic orthogonal involution on a central simple algebra over a field of characteristic $\ne2$ remains non-hyperbolic over some splitting field of the algebra.

2010 Mathematics Subject Classification: 14L17; 14C25

Keywords and Phrases: Algebraic groups, involutions, projective homogeneous varieties, Chow groups and motives, Steenrod operations.

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