Geometry & Topology

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

Marc Levine

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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.

Article information

Source
Geom. Topol., Volume 19, Number 5 (2015), 2691-2740.

Dates
Received: 17 November 2013
Revised: 8 August 2014
Accepted: 6 September 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510858847

Digital Object Identifier
doi:10.2140/gt.2015.19.2691

Mathematical Reviews number (MathSciNet)
MR3416112

Zentralblatt MATH identifier
06503551

Subjects
Primary: 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15] 55T15: Adams spectral sequences
Secondary: 55P42: Stable homotopy theory, spectra

Keywords
Morel–Voevodsky stable homotopy category slice tower Adams–Novikov spectral sequence

Citation

Levine, Marc. The Adams–Novikov spectral sequence and Voevodsky's slice tower. Geom. Topol. 19 (2015), no. 5, 2691--2740. doi:10.2140/gt.2015.19.2691. https://projecteuclid.org/euclid.gt/1510858847


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