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

Marc Levine
Geometry & Topology 19 (2015) 2691–2740
DOI: 10.2140/gt.2015.19.2691
Abstract

We show that the spectral sequence induced by the Betti realization of the slice tower for the motivic sphere spectrum agrees with the Adams–Novikov spectral sequence, after a suitable reindexing. The proof relies on a partial extension of Deligne’s décalage construction to the Tot–tower of a cosimplicial spectrum.

Keywords
Morel–Voevodsky stable homotopy category, slice tower, Adams–Novikov spectral sequence
Mathematical Subject Classification 2010
Primary: 14F42, 55T15
Secondary: 55P42
References
Publication
Received: 17 November 2013
Revised: 8 August 2014
Accepted: 6 September 2014
Published: 20 October 2015
Proposed: Haynes Miller
Seconded: Paul Goerss, Bill Dwyer
Authors
Marc Levine
Fakultät Mathematik, Campus Essen
Universität Duisburg-Essen
45117 Essen
Germany
http://www.esaga.uni-due.de/marc.levine/