#### Volume 17, issue 4 (2017)

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An algebraic model for commutative $H\mskip-1mu\mathbb{Z}$–algebras

### Birgit Richter and Brooke Shipley

Algebraic & Geometric Topology 17 (2017) 2013–2038
##### Abstract

We show that the homotopy category of commutative algebra spectra over the Eilenberg–Mac Lane spectrum of an arbitrary commutative ring $R$ is equivalent to the homotopy category of ${E}_{\infty }$–monoids in unbounded chain complexes over $R$. 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.

##### Keywords
Eilenberg–Mac Lane spectra, symmetric spectra, $E_\infty$–differential graded algebras, Dold–Kan correspondence
Primary: 55P43
##### Publication
Revised: 9 December 2016
Accepted: 11 January 2017
Published: 3 August 2017
##### Authors
 Birgit Richter Department Mathematik Universität Hamburg Hamburg Germany http://www.math.uni-hamburg.de/home/richter/ Brooke Shipley Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago Chicago, IL United States http://homepages.math.uic.edu/~bshipley/