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The
Picard group of topological modular forms via descent
theory
Akhil Mathew and Vesna Stojanoska |
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Geometry & Topology 20 (2016) 3133–3217
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Abstract |
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This paper starts with an exposition of descent-theoretic techniques in the study of Picard groups of –ring spectra, which naturally lead to the study of Picard spectra. We then develop tools for the efficient and explicit determination of differentials in the associated descent spectral sequences for the Picard spectra thus obtained. As a major application, we calculate the Picard groups of the periodic spectrum of topological modular forms and the nonperiodic and nonconnective . We find that is cyclic of order , generated by the suspension (a result originally due to Hopkins), while . In particular, we show that there exists an invertible –module which is not equivalent to a suspension of . |
Keywords
Picard groups and spectra, descent, topological modular
forms
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Mathematical Subject Classification 2010
Primary: 14C22, 55N34, 55P43, 55S35, 55T99
Secondary: 55P47
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References |
Publication
Received: 22 October 2014
Revised: 8 October 2015
Accepted: 19 November 2015
Published: 21 December 2016
Proposed: Mark Behrens
Seconded: Haynes Miller, Jesper Grodal
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Authors |
| Akhil Mathew | |
| Department of Mathematics Harvard University One Oxford Street Cambridge, MA 02138 United States |
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| Vesna Stojanoska | |
| Department of Mathematics University of Illinois at Urbana-Champaign 1409 W Green Steet Urbana, IL 61801 United States |
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