Journal of the Ramanujan Mathematical Society

Volume 28, Issue 2, June 2013 pp. 213–222.

Orthogonal and symplectic grassmannians of division algebras

Authors: Nikita A. Karpenko
Author institution: Université Pierre et Marie Curie, Institute de Mathématiques de Jussieu, Paris, France

Summary: 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.

Contents Full-Text PDF