New York Journal of Mathematics
Volume 28 (2022), 1042-1056


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.

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.


The second author was supported in part by Simons Foundation: Collaboration Grants for Mathematicians #638247 and AFOSR grant FA9550-16-1-0212.

Author information

Crichton Ogle:
Department of Mathematics
The Ohio State University
231 West 18th Ave, Columbus, OH 43210, USA


Nikolas Schonsheck:
Department of Mathematical Sciences
University of Delaware
501 Ewing Hall, Newark, DE 19716, USA