Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-08T13:24:57.063Z Has data issue: false hasContentIssue false

Generically split projective homogeneous varieties. II

Published online by Cambridge University Press:  07 February 2012

Victor Petrov
Affiliation:
Johannes Gutenberg-Universität Mainz, Institut für Mathematik, Staudingerweg 9, D-55099 Mainz, [email protected]
Nikita Semenov
Affiliation:
Johannes Gutenberg-Universität Mainz, Institut für Mathematik, Staudingerweg 9, D-55099 Mainz, [email protected]
Get access

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].

Type
Research Article
Copyright
Copyright © ISOPP 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bri97.Brion, M., Equivariant cohomology and equivariant intersection theory, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 514, Representation theories and algebraic geometry (Montreal, 1997), 137, Kluwer Acad. Publ., Dordrecht, 1998.Google Scholar
Ch10.Chernousov, V., On the kernel of the Rost invariant for E8modulo 3, In Quadratic Forms, Linear Algebraic Groups, and Cohomology, Developments in Mathematics 18 (2010), Part 2, 199214.Google Scholar
Gr58.Grothendieck, A., La torsion homologique et les sections rationnelles, Exposé 5 in Anneaux de Chow et applications, Séminaire C. Chevalley, 2e année (1958).Google Scholar
Kc85.Kac, V., Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups, Invent. Math. 80 (1985), 6979.Google Scholar
PS10.Petrov, V., Semenov, N., Generically split projective homogeneous varieties, Duke Math. J. 152 (2010), 155173.Google Scholar
PSZ08.Petrov, V., Semenov, N., Zainoulline, K., J-invariant of linear algebraic groups, Ann. Sci. Éc. Norm. Sup. 41 (2008), no 6, 10231053.Google Scholar
QSZ.Quéguiner-Mathieu, A., Semenov, N., Zainoulline, K., The J-invariant, Tits algebras and triality, Preprint 2011, available from http://arxiv.org/abs/1104.1096.Google Scholar