On Hopkins' Picard groups for the prime 3 and chromatic level 2

Abstract

We give a calculation of Picard groups of K(2)-local invertible spectra and of E(2)-local invertible spectra, both at the prime 3. The main contribution of this paper is to calculation the subgroup of invertible spectra with the same Morava module as a sphere.

References in corpus (1)

• The rational homotopy of the K(2)-local sphere and the chromatic splitting conjecture for the prime 3 and level 2

Cited by in corpus (13)

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• A higher chromatic analogue of the image of J
• Chromatic Cyclotomic Extensions
• Picard groups and duality for Real Morava $E$-theories
• Coalgebraic Formal Curve Spectra and the Annular Tower
• The topological modular forms of $\mathbb{R}{P}^2$ and $\mathbb{R}{P}^2\wedge \mathbb{C}{P}^2$
• The ${\mathrm{Sp}}_{k,n}$-local stable homotopy category
• Exotic Picard groups and chromatic vanishing via the Gross-Hopkins duality
• Comparing Dualities in the $K(n)$-local Category
• The inverse limit topology and profinite descent on Picard groups in $K(n)$-local homotopy theory