Higher Hochschild cohomology of the Lubin–Tate ring spectrum

Abstract

We construct a spectral sequence computing factorization homology of an ${\mathcal{ℰ}}_d$–algebra in spectra using as an input an algebraic version of higher Hochschild homology due to Pirashvili. This induces a full computation of higher Hochschild cohomology when the algebra is étale. As an application, we compute higher Hochschild cohomology of the Lubin–Tate ring spectrum.