An algebraic model for commutative Hℤ–algebras

Richter, Birgit; Shipley, Brooke

doi:10.2140/agt.2017.17.2013

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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

DOI: 10.2140/agt.2017.17.2013

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

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/

Volume 17, issue 4 (2017)