Algebraic & Geometric Topology

Higher Hochschild cohomology of the Lubin–Tate ring spectrum

Geoffroy Horel

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Abstract

We construct a spectral sequence computing factorization homology of an 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.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3215-3252.

Dates
Received: 17 March 2014
Revised: 24 March 2015
Accepted: 6 April 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841066

Digital Object Identifier
doi:10.2140/agt.2015.15.3215

Mathematical Reviews number (MathSciNet)
MR3450760

Zentralblatt MATH identifier
1332.55004

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 55P48: Loop space machines, operads [See also 18D50]

Keywords
factorization homology Hochschild cohomology little disk operad Morava $E$ theory Lubin–Tate spectrum spectral sequence

Citation

Horel, Geoffroy. Higher Hochschild cohomology of the Lubin–Tate ring spectrum. Algebr. Geom. Topol. 15 (2015), no. 6, 3215--3252. doi:10.2140/agt.2015.15.3215. https://projecteuclid.org/euclid.agt/1510841066


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