# An algebraic model for commutative Hℤ–algebras

@article{Richter2014AnAM, title={An algebraic model for commutative Hℤ–algebras}, author={Birgit Richter and Brooke E. Shipley}, journal={Algebraic \& Geometric Topology}, year={2014}, volume={17}, pages={2013-2038} }

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.

## 39 Citations

An algebraic model for rational naive-commutative equivariant ring spectra

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Equipping a non-equivariant topological E_\infty operad with the trivial G-action gives an operad in G-spaces. The algebra structure encoded by this operad in G-spectra is characterised homotopically…

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A model for genuine equivariant commutative ring spectra away from the group order

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We use geometric fixed points to describe the homotopy theory of genuine equivariant commutative ring spectra after inverting the group order. The main innovation is the use of the extra structure…

Flatness and Shipley’s algebraicization theorem

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- 2020

We provide an enhancement of Shipley's algebraicization theorem which behaves better in the context of commutative algebras. This involves defining flat model structures as in Shipley and…

Monoidal Structures

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Our goal in this talk is to build the stable homotopy category as a symmetric monoidal category with the smash product. We define monoidal structures in Section 1. We then talk about the symmetric…

Commutative ring spectra

- Mathematics
- 2017

In this survey paper on commutative ring spectra we present some basic features of commutative ring spectra and discuss model category structures. As a first interesting class of examples of such…

Genuine-commutative ring structure on rational equivariant $K$-theory for finite abelian groups.

- Mathematics
- 2021

In this paper, we build on the work from our previous paper (arXiv:2002.01556) to show that periodic rational $G$-equivariant topological $K$-theory has a unique genuine-commutative ring structure…

Correction to: An algebraic model for rational naïve-commutative ring SO(2)-spectra and equivariant elliptic cohomology

- MathematicsMathematische Zeitschrift
- 2020

Equipping a non-equivariant topological $$\text {E}_\infty $$
E
∞
-operad with the trivial G-action gives an operad in G-spaces. For a G-spectrum, being an algebra over this operad does not…

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