Nikita A. Karpenko: Unitary Grassmannians of division algebras

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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.

Full text: dvi.gz 24 k, dvi 56 k, ps.gz 722 k, pdf.gz 134 k, pdf 150 k.

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