Mod-p acyclic spectra and p-inversion locality

Observation 7.3.2. Note that \(X \otimes \S /p \simeq X/p\) for every \(X\). In particular, a spectrum \(X\) is \(\S /p\)-acyclic if and only if the map \(p\colon X \to X\) is an isomorphism, i.e. \(X\) is \(\S [\frac {1}{p}]\)-local by Lemma 7.2.8.