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15 March 2010 Generically split projective homogeneous varieties
Viktor Petrov, Nikita Semenov
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Duke Math. J. 152(1): 155-173 (15 March 2010). DOI: 10.1215/00127094-2010-010

Abstract

Let G be an exceptional simple algebraic group over a field k, and let X be a projective G-homogeneous variety such that G splits over k(X). We classify such varieties X. This classification allows us to relate the Rost invariant of groups of type E7 and their isotropy and to give a two-line proof of the triviality of the kernel of the Rost invariant for such groups. Apart from this, it plays a crucial role in the solution of a problem posed by Serre for groups of type E8

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Viktor Petrov. Nikita Semenov. "Generically split projective homogeneous varieties." Duke Math. J. 152 (1) 155 - 173, 15 March 2010. https://doi.org/10.1215/00127094-2010-010

Information

Published: 15 March 2010
First available in Project Euclid: 11 March 2010

zbMATH: 1202.14045
MathSciNet: MR2643059
Digital Object Identifier: 10.1215/00127094-2010-010

Subjects:
Primary: 20G15
Secondary: 14L35

Rights: Copyright © 2010 Duke University Press

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Vol.152 • No. 1 • 15 March 2010
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