Geodesic
On the orientability of the slice filtration
Homology, homotopy, and applications, Tome 13 (2011) no. 2, pp. 293-300.

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

Let $X$ be a Noetherian separated scheme of finite Krull dimension. We show that the layers of the slice filtration in the motivic stable homotopy category $\mathcal{SH}$ are strict modules over Voevodsky’s algebraic cobordism spectrum. We also show that the zero slice of any commutative ring spectrum in $\mathcal{SH}$ is an oriented ring spectrum in the sense of Morel, and that its associated formal group law is additive. As a consequence, we deduce that with rational coefficients the slices are in fact motives in the sense of Cisinski-Déglise and have transfers if the base scheme is excellent. This proves a conjecture of Voevodsky.
DOI : 10.4310/HHA.2011.v13.n2.a17
Classification : 14F42, 55N22
Keywords: algebraic cobordism, $K$-theory, mixed motive, oriented cohomology theory, rigid homotopy group, slice filtration, transfer 
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     title = {On the orientability of the slice filtration},
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     pages = {293--300},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2011.v13.n2.a17/}
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Pablo Pelaez. On the orientability of the slice filtration. Homology, homotopy, and applications, Tome 13 (2011) no. 2, pp. 293-300. doi : 10.4310/HHA.2011.v13.n2.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2011.v13.n2.a17/

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