An algebraic model for commutative HZ-algebras

TL;DR

This paper establishes an equivalence between the homotopy category of commutative algebra spectra over the integers and E-infinity-monoids in chain complexes, using a series of Quillen equivalences.

Contribution

It introduces a new algebraic model linking commutative HZ-algebras with E-infinity-monoids in chain complexes via Quillen equivalences.

Findings

Homotopy categories are equivalent through Quillen equivalences.

Provides a new algebraic framework for commutative HZ-algebras.

Connects spectra with algebraic structures in chain complexes.

Abstract

We show that the homotopy category of commutative algebra spectra over the Eilenberg-Mac Lane spectrum of the integers is equivalent to the homotopy category of E-infinity-monoids in unbounded chain complexes. We do this by establishing a chain of Quillen equivalences between the corresponding model categories. We also provide a Quillen equivalence to commutative monoids in the category of functors from the category of finite sets and injections to unbounded chain complexes.