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6
votes
Accepted
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 $ …