2026-09-23T11:42:21Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/124687 2026-01-14 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Stojanoska, Vesna Rezk, Charles Berwick-Evans, Daniel McCarthy, Randy 2024-05 application/pdf en text Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2026-05-01 The student, Venkata Sai Narayana Bavisetty, accepted the attached license on 2024-04-23 at 07:30. The student, Venkata Sai Narayana Bavisetty, submitted this Dissertation for approval on 2024-04-23 at 07:41. This Dissertation was approved for publication on 2024-04-23 at 16:29. DSpace SAF Submission Ingestion Package generated from Vireo submission #20563 on 2024-09-16 at 00:50:06 Descent and Picard group of Q(2) Bavisetty, Venkata Sai Narayana 2024-04-23 Homotopy Theory Topological Modular Forms 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. Text eng https://hdl.handle.net/2142/124687 Copyright 2024 Venkata Sai Narayana Bavisetty Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics