Volume 10, issue 1 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On Hopkins' Picard group $\mathrm{Pic}_2$ at the prime $3$

Nasko Karamanov

Algebraic & Geometric Topology 10 (2010) 275–292
Abstract

In this paper we calculate the algebraic Hopkins Picard group Pic2alg 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 2000
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
Nasko Karamanov
Augsburger Strasse 36E
93051 Regensburg
Germany