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.

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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