Victor Petrov, Nikita Semenov, Kirill Zainoulline: Chow motives of generically split varieties

Submission: 2006, Jul 21

Let G be an anisotropic linear algebraic group which splits by a field extension of a prime degree. Let X be a projective homogeneous G-variety such that G splits over the function field of X. We prove that under certain conditions the Chow motive of X is isomorphic to a direct sum of twisted copies of an indecomposable motive R. This covers all known examples of motivic decompositions of generically split projective homogeneous varieties (Severi-Brauer varieties, Pfister quadrics, maximal orthogonal Grassmannians) as well as provides new ones (exceptional varieties of types E6 and E8).

2000 Mathematics Subject Classification: 14C15; 14M15

Keywords and Phrases: projective homogeneous variety, Chow motive

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