Levine, Marc

Slices and transfers

Doc. Math. (Bielefeld) Extra Vol. Andrei A. Suslin's Sixtieth Birthday, 393-443 (2010)


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.

Mathematics Subject Classification

14F42, 19E15, 19E08, 14C25, 55P42


algebraic cycles, Morel-Voevodsky stable homotopy category, slice filtration