The localisation L^f_n is compactly central, and the compactly central localisations of spectra are exactly the finite ones that are the identity away from finitely many primes.
Nilpotence and Stable Homotopy Theory II
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A strong finiteness condition for smashing localisations
The localisation L^f_n is compactly central, and the compactly central localisations of spectra are exactly the finite ones that are the identity away from finitely many primes.