Slices and Transfers

Abstract

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 ℙ¹-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.