karpenko at ualberta.ca
Submission: 2014, Aug 22
We consider a central division algebra over a separable quadratic extension of a base field endowed with a unitary involution and prove 2-incompressibility of certain varieties of isotropic right ideals of the algebra. The remaining related projective homogeneous varieties are shown to be 2-compressible in general. Together with [1], where a similar issue for orthogonal and symplectic involutions has been treated, the present paper completes the study of grassmannians of isotropic ideals of division algebras.
[1] Karpenko, N. A. Orthogonal and symplectic Grassmannians of division algebras. J. Ramanujan Math. Soc. 28 (2013), no. 2, 213--222.
2010 Mathematics Subject Classification: 14L17; 14C25
Keywords and Phrases: Algebraic groups, quadratic forms, projective homogeneous varieties, Chow groups and motives.
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