Geodesic
Motives and oriented cohomology of generically cellular varieties
Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 275-288.

Voir la notice de l'article provenant de la source International Press of Boston

For a cellular variety $X$ over a field $k$ of characteristic 0 and an algebraic oriented cohomology theory $\mathtt{h}$ of Levine-Morel we construct a filtration on the cohomology ring $\mathtt{h}(X)$ such that the associated graded ring is isomorphic to the Chow ring of $X$. Using this filtration we establish the following comparison result between Chow motives and $\mathtt{h}$-motives of generically cellular varieties: any irreducible Chow-motivic decomposition of a generically cellular variety $Y$ gives rise to an $\mathtt{h}$-motivic decomposition of $Y$ with the same generating function. Moreover, under some conditions on the coefficient ring of $\mathtt{h}$ the obtained $\mathtt{h}$-motivic decomposition will be irreducible. We also prove that if the Chow motives of two twisted forms of $Y$ coincide, then their $\mathtt{h}$-motives coincide as well.
DOI : 10.4310/HHA.2014.v16.n2.a15
Classification : 14F43, 20G10
Keywords: flag variety, oriented cohomology theory, algebraic group, algebraic cobordism 
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     pages = {275--288},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a15/}
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Alexander Neshitov. Motives and oriented cohomology of generically cellular varieties. Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 275-288. doi : 10.4310/HHA.2014.v16.n2.a15. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a15/

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