Geodesic
Motivic splitting lemma
Documenta mathematica, Tome 13 (2008), pp. 81-96
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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 that over the generic point of X the motives M and N become isomorphic to a direct sum of twisted Tate motives. The main result of the paper says that if a morphism f:M→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.
DOI : 10.4171/dm/242
Mots-clés : Chow motive, homogeneous variety 
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     author = {A. Vishik and K. Zainoulline},
     title = {Motivic splitting lemma},
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     doi = {10.4171/dm/242},
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A. Vishik; K. Zainoulline. Motivic splitting lemma. Documenta mathematica, Tome 13 (2008), pp. 81-96. doi: 10.4171/dm/242

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