$I_n$-Local Johnson-Wilson Spectra and their Hopf Algebroids

We consider a generalization $\mathcal{E}(n)$ of the Johnson-Wilson spectrum $E(n)$ for which $\mathcal{E}(n)_*$ is a local ring with maximal ideal $I_n$. We prove that the spectra $E(n)$, $\mathcal{E}(n)$ and $\widehat{E(n)}$ are Bousfield equivalent. We also show that the Hopf algebroid $\mathcal{E}(n)_*\mathcal{E}(n)$ is a free $\mathcal{E}(n)_*$-module, generalizing a result of Adams and Clarke for $KU_*KU$.

1991 Mathematics Subject Classification: Primary 55N20 55N22

Keywords and Phrases: Johnson-Wilson spectrum, Hopf algebroid, localization, free module

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