$I_n$-local Johnson-Wilson spectra and their Hopf algebroids

Abstract

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 .