MULTIPLICATIVE PROPERTIES OF THE SLICE FILTRATION

作者：Pelaez Pablo^*

来源：Asterisque, 2011, (335): VII-+.

Let S be a Noetherian separated scheme of finite Krull dimension, and &H(S) be the rnotivic stable hornotopy category of Morel-Voevodsky. In order to get a motivic analogue of the Postnikov tower, Voevodsky [25] constructs the slice filtration by filtering &H(S) with respect to the smash powers of the multiplicative group G.,. We show that the slice filtration is compatible with the smash product in Jardine's category Spt(T)(Sigma)M(*) of motivic symmetric T-spectra [14], and describe several interesting consequences that follow from this compatibility. Among them, we have that over a perfect field all the slices s(q) are in a canonical way modules in Spt(T)(Sigma)M(*), over the motivic Eilenberg-MacLane spectrum HZ, and if the field has characteristic zero it follows that the slices sq are big motives in the sense of Voevodsky, this relies on the work of Levine [16], Rondigs-Ostwer [22] and Voevodsky [26]. It also follows that the smash product in Sppt(T)(Sigma)M(*) induces pairings in the rnotivic Atiyah-Hirzebruch spectral sequence.

• 出版日期2011