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Crichton Ogle and
Nikolas Schonsheck
On the chromatic localization of the homotopy completion tower for O-algebras
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| Published: |
July 23, 2022. |
| Keywords: |
Ring spectra, chromatic localization, homotopy completion, functor calculus, operads. |
| Subject [2010]: |
55P43, 55P48, 55P60, 55U35, 18G55. |
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Abstract
The completion tower of a nonunital commutative ring is a classical construction in commutative algebra. In the setting of structured ring spectra as modeled by algebras over a spectral operad, the analogous construction is the homotopy completion tower. The purpose of this brief note is to show that smashing localizations, such as that given by the Johnson-Wilson spectrum E(n), commute with the terms of this tower.
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| Acknowledgements
The second author was supported in part by Simons Foundation: Collaboration Grants for Mathematicians #638247 and AFOSR grant FA9550-16-1-0212.
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| Author information
Crichton Ogle:
Department of Mathematics
The Ohio State University
231 West 18th Ave, Columbus, OH 43210, USA
ogle.1@osu.edu
Nikolas Schonsheck:
Department of Mathematical Sciences
University of Delaware
501 Ewing Hall, Newark, DE 19716, USA
nischon@udel.edu
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