Algebraic & Geometric Topology 10 (2010) 275–292

DOI: 10.2140/agt.2010.10.275

Abstract

In this paper we calculate the algebraic Hopkins Picard group Pic₂^alg at the prime p = 3, which is a subgroup of the group of isomorphism classes of invertible K(2)–local spectra, ie of Hopkins’ Picard group Pic₂. We use the resolution of the K(2)–local sphere introduced by Goerss, Henn, Mahowald and Rezk in [Ann. of Math (2) 162 (2005) 777-822] and the methods from Henn, Karamanov and Mahowald [to appear in Math. Zeit. arXiv:0811.0235] and Karamanov [PhD thesis, Universite Louis Pasteur (2006)].

Keywords

Hopkins Picard group, Morava K–theory, K(2)–local sphere

Mathematical Subject Classification

Primary: 55N22, 55P42, 55Q10, 55Q51, 55Q52

References

Publication

Received: 30 March 2009
Revised: 20 November 2009
Accepted: 24 November 2009
Published: 12 February 2010

Authors