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 décalage construction to the Tot-tower of a cosimplicial spectrum.

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 "décalage" technique applies

References in corpus (3)

• From algebraic cobordism to motivic cohomology
• A comparison of motivic and classical homotopy theories
• Galois equivariance and stable motivic homotopy theory

Cited by in corpus (8)

• The $C_2$-effective spectral sequence for $C_2$-equivariant connective real $K$-theory
• An extension in the Adams spectral sequence in dimension 54
• $\mathbb{R}$-motivic $v_1$-periodic homotopy
• Morava K-theory and Filtrations by Powers
• Galois reconstruction of Artin-Tate $\mathbb{R}$-motivic spectra
• Transchromatic extensions in motivic and Real bordism
• Moduli stack of oriented formal groups and cellular motivic spectra over $\mathbf{C}$
• The second stable homotopy groups of motivic spheres