Picard Groups of Some Local Categories

  • Yousuke Kamiya

    2-17, Imazuyama-Naka, Hyogo, Japan
  • Katsumi Shimomura

    Kochi University, Japan

Abstract

For each -local spectrum , denotes the full subcategory consisting of -local spectra of the category of -local spectra. The Picard group is the collection of isomorphism classes of invertible spectra in . If this is a set, it is a group with multiplication defined by the smash product. We show that if a spectrum satisfies a relation of the Bousfield classes, then . In particular, if 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. 303–314

DOI 10.2977/PRIMS/1201011783