University of Illinois Urbana-Champaign

Descent and Picard group of Q(2)

Bavisetty, Venkata Sai Narayana

This item's files can only be accessed by the System Administrators group.

Permalink

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

Description

Title
Descent and Picard group of Q(2)
Author(s)
Bavisetty, Venkata Sai Narayana
Issue Date
2024-04-23
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
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.
Graduation Semester
2024-05
Type of Resource
Thesis
Copyright and License Information
Copyright 2024 Venkata Sai Narayana Bavisetty

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois