Slices and Transfers

We study Voevodsky's slice tower for $S^1$-spectra, and raise a number of questions regarding its properties. We show that the 0th slice does not in general admit transfers, although it does for a $\P^1$-loop-spectrum. We define a new tower for each of the higher slices, and show that the layers in these towers have the structure of Eilenberg-Maclane spectra on effective motives.

2010 Mathematics Subject Classification: Primary 14F42, 19E15; Secondary 19E08, 14C25, 55P42

Keywords and Phrases: Algebraic cycles, Morel-Voevodsky stable homotopy category, slice filtration

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