Picard groups and duality for Real Morava $E$-theories

Abstract

We show, at the prime 2, that the Picard group of invertible modules over $E_n^{h{C}_2}$ is cyclic. Here, $E_n$ is the height $n$ Lubin--Tate spectrum and its $C_2$-action is induced from the formal inverse of its associated formal group law. We further show that $E_n^{h{C}_2}$ is Gross--Hopkins self-dual and determine the exact shift. Our results generalize the well-known results when $n=1$.

v3: Version to appear Algebraic and Geometric Topology

References in corpus (5)

• Topological resolutions in K(2)-local homotopy theory at the prime 2
• Gorenstein duality for Real spectra
• Picard groups of higher real $K$-theory spectra at height $p-1$
• Invertible $K(2)$-Local $E$-Modules in $C_4$-Spectra
• Gross-Hopkins Duals of Higher Real K-theory Spectra

Cited by in corpus (1)

• Odd primary analogs of Real orientations