Hyperbolicity of unitary involutions

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...

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Bibliographic Details
Published in:	Science China. Mathematics Vol. 55; no. 5; pp. 937 - 945
Main Author:	Karpenko, Nikita A.
Format:	Journal Article
Language:	English
Published:	Heidelberg SP Science China Press 01-05-2012
Subjects:	Applications of Mathematics China Incompressibility Mathematical analysis Mathematics Mathematics and Statistics Proving Theorems 不可压缩性双曲同构定理对合正交类似证明 Chow groups and motives 14L17 14C25 projective homogeneous varieties Algebraic groups involutions Steenrod operations
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Summary:	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.
Bibliography:	algebraic groups; involutions; projective homogeneous varieties; Chow groups and motives; Steenrod operations KARPENKO Nikita A.Institut de Math＇ematiques de Jussieu,Universit＇e Pierre et Marie Curie,Paris,France 11-1787/N 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. ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	1674-7283 1869-1862
DOI:	10.1007/s11425-012-4364-4