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arXiv · 1810.05439

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

Drew Heard·Guchuan Li·XiaoLin Danny Shi
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Abstract

We show, at the prime 2, that the Picard group of invertible modules over $E_n^{hC_2}$ 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 $E_n^{hC_2}$ is Gross--Hopkins self-dual and determine the exact shift. Our results generalize the well-known results when $n = 1$.

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Drew Heard, Guchuan Li, XiaoLin Danny Shi. 2018-10-12. Picard groups and duality for Real Morava $E$-theories. https://doi.org/10.2140/agt.2021.21.2703

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