Homology, Homotopy and Applications

Volume 13 (2011)

Number 2

On the orientability of the slice filtration

Pages: 293 – 300

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n2.a17


Pablo Pelaez (Universität Duisburg-Essen, Mathematik, Essen, Germany)


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.


algebraic cobordism; $K$-theory; mixed motive; oriented cohomology theory; rigid homotopy group; slice filtration; transfer

2010 Mathematics Subject Classification

14F42, 55N22

Published 25 January 2012