p-complete spectra

Definition 7.3.1. Consider the mod \(p\) Moore spectrum \(\S /p\), defined as the cofiber \[ \S /p \quad := \quad \cofib (p\colon \S \to \S ). \] We refer to an \(\S /p\)-local spectrum as \(p\)-complete. We write \[ \Sp ^{\wedge }_p \subseteq \Sp \] for the full subcategory of \(p\)-complete spectra, and denote the resulting localization functor by \[ (-)^{\wedge }_p := L_{\S /p} \colon \Sp \to \Sp ^{\wedge }_p. \]