#### Volume 21, issue 6 (2021)

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Picard groups and duality for real Morava $E$–theories

### Drew Heard, Guchuan Li and XiaoLin Danny Shi

Algebraic & Geometric Topology 21 (2021) 2703–2760
##### 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 $n=1$.

##### Keywords
chromatic homotopy, Picard group, Brown–Comenetz, Morava, Gross–Hopkins, real K–theory
##### Mathematical Subject Classification 2010
Primary: 14C22, 19L99, 55P91, 55U30
Secondary: 55N20, 55P43