Truncated Derived Functors and Spectral Sequences

TL;DR

This paper explores how higher terms of spectral sequences, including the Adams spectral sequence, are determined by truncations of relative derived functors associated with mapping algebras, providing a unified framework.

Contribution

It introduces a method to understand higher spectral sequence terms through truncations of relative derived functors linked to simplicial mapping algebras.

Findings

Higher spectral sequence terms are governed by truncations of relative derived functors.

The approach applies to various spectral sequences beyond Adams.

Provides a new perspective on the algebraic structure of spectral sequences.

Abstract

The $E_2$ term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for a number of other spectral sequences. Our goal is to show how the higher terms of such spectral sequences are determined by truncations of relative derived functors, defined in terms of certain simplicial functors called mapping algebras