karpenko at math.jussieu.fr, zhykhovich at math.jussieu.fr

Submission: 2011, Mar 15

We prove the so-called Unitary Isotropy Theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal, symplectic, and unitary involutions are formal consequences of this theorem. A component of the proof is a detailed study of the quasi-split unitary grassmannians.

2010 Mathematics Subject Classification: 14L17; 14C25

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

Full text: dvi.gz 51 k, dvi 122 k, ps.gz 965 k, pdf.gz 232 k, pdf 280 k.

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