On the chromatic localization of the homotopy completion tower for $\mathcal{O}$-algebras
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 $E(n)$ commutes with the terms of this tower.
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Algebraic Topology
55P43, 55P48, 55P60, 55U35, 18G55
