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 $n=1$.

arXiv commentv3: Version to appear Algebraic and Geometric Topology

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• Odd primary analogs of Real orientations