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On motivic decompositions arising from the method of Białynicki-Birula

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Recently, V. Chernousov, S. Gille and A. Merkurjev have obtained a decomposition of the motive of an isotropic smooth projective homogeneous variety analogous to the Bruhat decomposition. Using the method of A. Białynicki-Birula and a corollary, which is essentially due to S. del Baño, I generalize this decomposition to the case of a (possibly anisotropic) smooth projective variety homogeneous under the action of an isotropic reductive group. This answers a question of N. Karpenko.

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  1. Department of Mathematics, SUNY at Buffalo, Buffalo, NY, 14260-2900, USA

    Patrick Brosnan

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Brosnan, P. On motivic decompositions arising from the method of Białynicki-Birula. Invent. math. 161, 91–111 (2005). https://doi.org/10.1007/s00222-004-0419-7

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