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

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.