For each p-local spectrum E, ℒ_E_ denotes the full subcategory consisting of E-local spectra of the category of p-local spectra. The Picard group Pic(ℒ_E_) is the collection of isomorphism classes of invertible spectra in ℒ_E_. If this is a set, it is a group with multiplication deﬁned by the smash product. We show that if a spectrum E satisﬁes a relation (E) ≥ H_ℤ/p of the Bousﬁeld classes, then Pic(ℒ_E) = ℤ. In particular, Pic(ℒ_E_) = ℤ if E is connective.
Cite this article
Yousuke Kamiya, Katsumi Shimomura, Picard Groups of Some Local Categories. Publ. Res. Inst. Math. Sci. 43 (2007), no. 2, pp. 303–314DOI 10.2977/PRIMS/1201011783