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Invertible $K(2)$–local
$E$–modules in $C_4$–spectra
Agnès Beaudry, Irina Bobkova, Michael Hill and Vesna Stojanoska |
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Algebraic & Geometric Topology 20 (2020) 3423–3503
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Abstract |
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We compute the Picard group of the category of –local module spectra over the ring spectrum , where is a height Morava –theory and is a subgroup of the associated Morava stabilizer group. This group can be identified with the Picard group of –local –modules in genuine –spectra. We show that in addition to a cyclic subgroup of order generated by , the Picard group contains a subgroup of order generated by , where is the sign representation of the group . In the process, we completely compute the –graded Mackey functor homotopy fixed point spectral sequence for the –spectrum . |
Keywords
chromatic homotopy theory, Morava E–theory, Picard groups,
higher real K–theory
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Mathematical Subject Classification 2010
Primary: 55P42, 55Q91
Secondary: 20J06, 55M05, 55P60, 55Q51
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References |
Publication
Received: 14 January 2019
Revised: 16 September 2019
Accepted: 22 October 2019
Published: 29 December 2020
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Authors |
| Agnès Beaudry | |
| Department of Mathematics University of Colorado Boulder Boulder, CO United States |
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| Irina Bobkova | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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| Michael Hill | |
| Department of Mathematics University of California, Los Angeles Los Angeles, CA United States |
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| Vesna Stojanoska | |
| Department of Mathematics University of Illinois at Urbana–Champaign Urbana, IL United States |
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