Geometry & Topology

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

Marc Levine

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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