Algebraic & Geometric Topology

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

Birgit Richter and Brooke Shipley

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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.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 4 (2017), 2013-2038.

Dates
Received: 29 September 2015
Revised: 9 December 2016
Accepted: 11 January 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841435

Digital Object Identifier
doi:10.2140/agt.2017.17.2013

Mathematical Reviews number (MathSciNet)
MR3685600

Zentralblatt MATH identifier
1381.55007

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)

Keywords
Eilenberg–Mac Lane spectra symmetric spectra $E_\infty$–differential graded algebras Dold–Kan correspondence

Citation

Richter, Birgit; Shipley, Brooke. An algebraic model for commutative $H\mskip-1mu\mathbb{Z}$–algebras. Algebr. Geom. Topol. 17 (2017), no. 4, 2013--2038. doi:10.2140/agt.2017.17.2013. https://projecteuclid.org/euclid.agt/1510841435


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