A Toda bracket convergence theorem for multiplicative spectral sequences

TL;DR

This paper generalizes Moss' theorem to a broad class of spectral sequences in symmetric monoidal stable categories, enabling new computational tools for motivic and other spectral sequences.

Contribution

It proves a general Toda bracket convergence theorem applicable to spectral sequences from monoidal filtrations, extending Moss' classical results.

Findings

Generalized Moss' theorem for symmetric monoidal categories

Applicable to motivic slice and Adams spectral sequences

Facilitates computations in motivic homotopy theory

Abstract

Moss' theorem, which relates Massey products in the $E_r$-page of the classical Adams spectral sequence to Toda brackets of homotopy groups, is one of the main tools for calculating Adams differentials. Working in an arbitrary symmetric monoidal stable topological model category, we prove a general version of Moss' theorem which applies to spectral sequences that arise from filtrations compatible with the monoidal structure. The theorem has broad applications, e.g. to the computation of the motivic slice and motivic Adams spectral sequences.