Journal of the Ramanujan Mathematical Society

Nikita A. Karpenko ¹

Affiliations
1 Universite Pierre et Marie Curie, Institute de Mathematiques de Jussieu, Paris, FR

Abstract

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.

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Nikita A. Karpenko ¹

Affiliations
1 WestMlische Wilhelms-Universitat, Mathematisches Institut, Einsteinstr. 62, D-48149 Munster, DE

Abstract

We show that an orthogonal involution of a central division algebra D (over a field of characteristic, not 2) remains anisotropic over the generic splitting field of D. We also give a couple of other applications of the same technique.

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