Geodesic
On the Picard group graded homotopy groups of a finite type two $K(2)$-local spectrum at the prime three
Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 177-203.

Voir la notice de l'article provenant de la source International Press of Boston

Consider Hopkins’ Picard group of the stable homotopy category of $E(2)$-local spectra at the prime three, consisting of homotopy classes of invertible spectra. Then, it is isomorphic to the direct sum of an infinite cyclic group and two cyclic groups of order three. We consider the Smith–Toda spectrum $V(1)$ and the cofiber $V_2$ of the square $\alpha^2$ of the Adams map, which is a ring spectrum. In this paper, we introduce imaginary elements which make computation clearer, and determine the module structures of the Picard group graded homotopy groups $\pi_\star (V (1))$ and $\pi_\star (V2)$.
DOI : 10.4310/HHA.2022.v24.n1.a10
Classification : 55P42, 55Q51, 55Q99, 55T15
Keywords: homotopy group, Adams–Novikov spectral sequence, Bousfield–Ravenel localization 
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     title = {On the {Picard} group graded homotopy groups of a finite type two $K(2)$-local spectrum at the prime three},
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Ippei Ichigi; Katsumi Shimomura. On the Picard group graded homotopy groups of a finite type two $K(2)$-local spectrum at the prime three. Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 177-203. doi : 10.4310/HHA.2022.v24.n1.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a10/

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