#### 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
##### Publication
Received: 17 March 2014
Revised: 24 March 2015
Accepted: 6 April 2015
Published: 12 January 2016
##### Authors
 Geoffroy Horel Mathematisches Institut Universität Münster Einsteinstrasse 62 D-48149 Münster Germany http://geoffroy.horel.org