In motivic homotopy theory, the slice filtration is a filtration of $\mathrm{H}(S)$ and of $SH(S)$ which is analogous to the Postnikov filtration for (∞,1)-topoi. It generalizes the coniveau filtration in algebraic K-theory, the fundamental filtration on Witt groups?, and the weight filtration on mixed Tate motives.
If $S$ is smooth over a field, the layers of the slice filtration of a motivic spectrum (called its slices) are modules over the motivic Eilenberg–Mac Lane spectrum $H(\mathbb{Z})$. At least if $S$ is a field of characteristic zero, this is the same thing as an integral motive. The spectral sequences associated to the slice filtration are analogous to the Atiyah-Hirzebruch spectral sequences in that their first page consists of motivic cohomology groups.
Vladimir Voevodsky, Open problems in the motivic stable homotopy theory, I, web.
Vladimir Voevodsky, A possible new approach to the motivic spectral sequence for algebraic K-theory, web.
Marc Levine, Motivic Postnikov towers, talk notes, 2007, pdf.
In the unstable motivic homotopy category?:
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