A conjecture of Colliot-Thelene in the case of the exceptional groups

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• Ivan Panin (St Petersburg)
• Wednesday 30 May 2012, 14:15-15:15
• MR 13, CMS.

If you have a question about this talk, please contact Burt Totaro.

We consider a regular local ring R containing an infinite field of characteristic different from 2, the fraction field K of R and a simple algebraic group scheme G over R. The question is whether for a given parabolic subgroup in the group G_K there is a parabolic subgroup scheme of the same type in G over R.

We answer the question in the affirmative provided that G has type G2, F4, or E6. If G is of type E7 or E8, then we answer the question in the affirmative for most types of parabolics. This partly solves a conjecture of Colliot-Thélène and extends an earlier result of I. Panin and K. Pimenov for quadratic spaces.

This is joint work with V. Petrov.

This talk is part of the Algebraic Geometry Seminar series.

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