Descent and Picard group of Q(2)

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Bavisetty, Venkata Sai Narayana

Contributors dc:contributor

• Stojanoska, Vesna
• Rezk, Charles
• Berwick-Evans, Daniel
• McCarthy, Randy

• Homotopy Theory
• Topological Modular Forms

Statement dc:rights

• Copyright 2024 Venkata Sai Narayana Bavisetty

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/124687

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F124687