Volume 15, issue 6 (2015)

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Higher Hochschild cohomology of the Lubin–Tate ring spectrum

Geoffroy Horel

Algebraic & Geometric Topology 15 (2015) 3215–3252
Abstract

We construct a spectral sequence computing factorization homology of an ${\mathsc{ℰ}}_{d}$–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.

Keywords
factorization homology, Hochschild cohomology, little disk operad, Morava $E$ theory, Lubin–Tate spectrum, spectral sequence
Mathematical Subject Classification 2010
Primary: 55P43
Secondary: 16E40, 55P48