On the chromatic localization of the homotopy completion tower for $\mathcal{O}$-algebras
Algebraic Topology
2022-07-26 v3
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 localization with respect to the Johnson-Wilson spectrum commutes with the terms of this tower.
Keywords
Cite
@article{arxiv.2012.10539,
title = {On the chromatic localization of the homotopy completion tower for $\mathcal{O}$-algebras},
author = {Crichton Ogle and Nikolas Schonsheck},
journal= {arXiv preprint arXiv:2012.10539},
year = {2022}
}
Comments
Updates based on referee report. Changes include expanded proofs in Section 4 on the classification of the Taylor tower and other updates to improve clarity and exposition. Published in New York Journal of Mathematics