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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–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.

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Keywords
Eilenberg–Mac Lane spectra, symmetric spectra, $E_\infty$–differential graded algebras, Dold–Kan correspondence
Mathematical Subject Classification 2010
Primary: 55P43
References
Publication
Received: 29 September 2015
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/