vishik@mccme.ru, kirill@mathematik.uni-muenchen.de

Submission: 2007, Jan 30

Let M be a Chow motive over a field F. Let X be a smooth projective variety over F and N be a direct summand of the motive of X. Assume the motives M and N split over the generic point of X as direct sums of shifted copies of a Tate motive. The main result of the paper says that if a morphism f: M \to N splits over the generic point of X then it splits over F, i.e., N is a direct summand of M. We apply this result to various examples of motives of projective homogeneous varieties.

2000 Mathematics Subject Classification: 14C15; 14M15

Keywords and Phrases: Motive, Rost Nilpotence Theorem

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