Nikita A. Karpenko: Hyperbolicity of unitary involutions

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Submission: 2010, Jul 30

We prove the so-called Unitary Hyperbolicity Theorem, a result on hyperbolicity of unitary involutions. The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one. While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties, the proof in the unitary case is based on the incompressibility of their Weil transfers.

2000 Mathematics Subject Classification: 14L17; 14C25

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

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