Tits construction and Rost invariant

Nikita Geldhauser; Victor Petrov

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arXiv · 2408.10969

Tits construction and Rost invariant

Nikita Geldhauser·Victor Petrov

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Abstract

We show a Springer type theorem for the variety of parabolic subgroups of type $1,2,6$ for all groups of type $E_6$. As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous varieties of type $^2E_6$ different from varieties of Borel subgroups. The proof combines several topics, notably the Rost invariant, a Tits construction, Cartan's symmetric spaces and indirectly the structure of the Chow motives of projective homogeneous varieties of exceptional type.

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Nikita Geldhauser, Victor Petrov. 2024-08-20. Tits construction and Rost invariant. https://arxiv.org/abs/2408.10969

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