Title: A Note on Hopkins' Picard Groups of the Stable Homotopy Categories of $L_n$-Local Spectra
Abstract:For a stable homotopy category, M. Hopkins introduced a Picard group as a category consisting of isomorphism classes of invertible objects. For the stable homotopy category of L_n -local spectra, M. H...For a stable homotopy category, M. Hopkins introduced a Picard group as a category consisting of isomorphism classes of invertible objects. For the stable homotopy category of L_n -local spectra, M. Hovey and H. Sadofsky showed that the Picard group is actually a group containing the group of integers as a direct summand. Kamiya and the author constructed an injection from the other summand of the Picard group to the direct sum of the E_r -terms E_r^{r,r-1} over r\ge 2 of the Adams–Novikov spectral sequence converging to the homotopy groups of the L_n -localized sphere spectrum. In this paper, we show in a classical way that the injection is a bijection under a condition.Read More
Publication Year: 2020
Publication Date: 2020-01-21
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 1
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