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Homotopy limit and Bousfield localization

Yes, $H\mathbb{F}_p$-localizations are $p$-complete. We have the cofiber sequence $$ \Sigma^{-1}\mathbb{S}/p^\infty \xrightarrow{j} \mathbb{S}\to \mathbb{S}[p^{-1}] \to \mathbb{S}/p^\infty $$ where $ …
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