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Smashing localizations in the category of spectra
The finite localization away from the thick subcategory of objects of type $n+1$ is sometimes written as $L_n^f$ or $L\prime_n$ (unless I've messed up the indexing). … One formulation of the telescope conjecture is that every smashing localization is a finite localization; in particular, if you write $L_n$ for localization with respect to $E_n$, then a consequence would …