The Adams-Novikov spectral sequence and Voevodsky's slice tower
Algebraic Geometry
2015-10-28 v3
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.
Keywords
Cite
@article{arxiv.1311.4179,
title = {The Adams-Novikov spectral sequence and Voevodsky's slice tower},
author = {Marc Levine},
journal= {arXiv preprint arXiv:1311.4179},
year = {2015}
}
Comments
Final version to appear in Geometry and Topology. Major changes: we require the base-scheme to be of the form Spec k, k a perfect field, at a number of points in the construction. This does not affect any of the main results relating the Adams-Novikov and slice spectral sequences, but does restrict the range of examples for which the "d\'ecalage" technique applies