Nikita A. Karpenko: Orthogonal and symplectic grassmannians of division algebras

karpenko at

Submission: 2012, May 21

We consider a central division algebra (over a field) endowed with a quadratic pair or with a symplectic involution and prove 2-incompressibility of certain varieties of isotropic right ideals of the algebra. This covers a recent conjecture raised by M. Zhykhovich. The remaining related projective homogeneous varieties are 2-compressible in general.

2010 Mathematics Subject Classification: 14L17; 14C25

Keywords and Phrases: Algebraic groups, quadratic forms, projective homogeneous varieties, Chow groups and motives.

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