Director of Research (if dissertation) or Advisor (if thesis)
Stojanoska, Vesna
Doctoral Committee Chair(s)
Rezk, Charles
Committee Member(s)
Berwick-Evans, Daniel
McCarthy, Randy
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Homotopy Theory
Topological Modular Forms
Language
eng
Abstract
For l a topological generator of the p-adic units, where p is any prime, Behrens [8] introduced a semi cosimplicial spectrum Q(l) which has a resolution constructed using topological modular forms, TMF, and related spectra. When p is 3 and l is 2, the spectrum Q(2) is closely related to the K(2)-local sphere. In my thesis, I investigate the Picard group of Q(l). I prove some descent and detection results for invertible Q(l)-modules. For computations, I restrict l to 2 at the prime 3, and using descent I calculate some elements in the Picard group of Q(2). I also prove detection results for the elements of Picard group of the K(2)-local category of spectra.
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