Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology

Research Article

Generically split projective homogeneous varieties. II

Victor Petrova1* and Nikita Semenova2*

a1 Johannes Gutenberg-Universität Mainz, Institut für Mathematik, Staudingerweg 9, D-55099 Mainz, Germany victorapetrov@googlemail.com

a2 Johannes Gutenberg-Universität Mainz, Institut für Mathematik, Staudingerweg 9, D-55099 Mainz, Germany semenov@uni-mainz.de

Abstract

This article gives a complete classification of generically split projective homogeneous varieties. This project was begun in our previous article [PS10], but here we remove all restrictions on the characteristic of the base field, give a new uniform proof that works in all cases and in particular includes the case PGO2n + which was missing in [PS10].

(Received October 21 2011)

Key Words

  • linear algebraic groups;
  • projective homogeneous varieties;
  • J-invariant

Footnotes

*   The authors gratefully acknowledge the hospitality and support of the Max-Planck Institute for Mathematics, Bonn, and the support of SFB/Transregio 45 (Bonn-Essen-Mainz). The first author was partially supported by Russian Foundation for Basic Research, grants 08-01-00756, 09-01-90304, 09-01-00878, 09-01-91333, 10-01-90016, and 10-01-92651.