On higher topological Hochschild homology of rings of integers

We determine higher topological Hochschild homology of rings of integers in number fields with coefficients in suitable residue fields. We use the iterative description of higher THH for this and Postnikov arguments that allow us to reduce the necessary computations to calculations in homological algebra, starting from the results of Bokstedt and Lindenstrauss-Madsen on (ordinary) topological Hochschild homology.

An algebraic model for commutative HZ-algebras

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.