Higher Hochschild cohomology of the Lubin–Tate ring spectrum

Abstract

We give a method for computing factorization homology of $\oper{E}_n$-algebra using as an input an algebraic version of higher Hochschild homology due to Pirashvili. We then show how to compute higher Hochschild homology and cohomology when the algebra is \'etale in a sense that we make precise. As an application, we compute higher Hochschild cohomology of the Lubin-Tate ring spectrum.