{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/124687"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/124687","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Descent and Picard group of Q(2)","abstract":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2026-05-01","abstract_html":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2026-05-01","abstract_has_math":false,"creators":["Bavisetty, Venkata Sai Narayana"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Stojanoska, Vesna","Rezk, Charles","Berwick-Evans, Daniel","McCarthy, Randy"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-05","date_published":"2024-05","updated_at":"2026-07-22T22:25:02Z","subjects":["Homotopy Theory","Topological Modular Forms"],"languages":["en","eng"],"rights":["Copyright 2024 Venkata Sai Narayana Bavisetty"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/124687","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stojanoska, Vesna","Rezk, Charles","Berwick-Evans, Daniel","McCarthy, Randy"]},{"key":"dc:creator","label":"Author","values":["Bavisetty, Venkata Sai Narayana"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-05","2024-04-23"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Homotopy Theory","Topological Modular Forms"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2024 Venkata Sai Narayana Bavisetty"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/124687"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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","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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Descent and Picard group of Q(2)"]}]}],"canonical_facts":{"dc:contributor":["Stojanoska, Vesna","Rezk, Charles","Berwick-Evans, Daniel","McCarthy, Randy"],"dc:creator":["Bavisetty, Venkata Sai Narayana"],"dc:date":["2024-05","2024-04-23"],"dc:description":["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","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."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/124687"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Venkata Sai Narayana Bavisetty"],"dc:subject":["Homotopy Theory","Topological Modular Forms"],"dc:title":["Descent and Picard group of Q(2)"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:02Z"}