The Adams–Novikov spectral sequence and Voevodsky’s slice tower

Abstract

We show that the spectral sequence converging to the stable homotopy groups of spheres, induced by the Betti realization of the slice tower for the motivic sphere spectrum, agrees with the Adams-Novikov spectral sequence, after a suitable re-indexing. The proof relies on an extension of Deligne's d\'ecalage construction to the Tot-tower of a cosimplicial spectrum.