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Picard groups and
duality for real Morava $E$–theories
Drew Heard, Guchuan Li and XiaoLin Danny Shi |
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Algebraic & Geometric Topology 21 (2021) 2703–2760
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Abstract |
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We show, at the prime 2, that the Picard group of invertible modules over is cyclic. Here, is the height Lubin–Tate spectrum and its –action is induced from the formal inverse of its associated formal group law. We further show that is Gross–Hopkins self-dual and determine the exact shift. Our results generalize the well-known results when . |
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Keywords
chromatic homotopy, Picard group, Brown–Comenetz, Morava,
Gross–Hopkins, real K–theory
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Mathematical Subject Classification 2010
Primary: 14C22, 19L99, 55P91, 55U30
Secondary: 55N20, 55P43
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References |
Publication
Received: 14 November 2018
Revised: 25 November 2019
Accepted: 12 October 2020
Published: 22 November 2021
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Authors |
| Drew Heard | |
| Department of Mathematical
Sciences Norwegian University of Science and Technology Trondheim Norway |
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| https://folk.ntnu.no/drewkh/ | |
| Guchuan Li | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| XiaoLin Danny Shi | |
| Department of Mathematics University of Chicago Chicago, IL United States |
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