{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/129886"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/129886","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Chromatic homotopy theory in HF_p based synthetic spectra","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_has_math":false,"creators":["Kundu, Abhra Abir"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rezk, Charles W.","Stojanoska, Vesna","Berwick-Evans, Daniel","Heller, Jeremiah"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-07-17","date_published":"2025-07-17","updated_at":"2026-07-22T22:25:06Z","subjects":["Homotopy Theory","Synthetic Spectra","Chromatic Homotopy Theory","Algebraic Topology"],"languages":["en","eng"],"rights":["Copyright 2025 Abhra Kundu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/129886","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rezk, Charles W.","Stojanoska, Vesna","Berwick-Evans, Daniel","Heller, Jeremiah"]},{"key":"dc:creator","label":"Author","values":["Kundu, Abhra Abir"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-07-17","2025-08"]},{"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 Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Homotopy Theory","Synthetic Spectra","Chromatic Homotopy Theory","Algebraic Topology"]}]},{"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 2025 Abhra Kundu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/129886"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","The student, Abhra Kundu, accepted the attached license on 2025-07-16 at 16:09.","The student, Abhra Kundu, submitted this Dissertation for approval on 2025-07-16 at 16:22.","This Dissertation was approved for publication on 2025-07-17 at 21:06.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22614 on 2025-10-20 at 16:58:41","In this dissertation, we introduce chromatic homotopy theory in the context of $H\\mathbb{F}_{p}$ based synthetic spectra. Then we study it by relating it to the classical chromatic homotopy theory of spectra and chromatic homotopy theory of its algebraic counterpart. Along the way we prove a version of Hopkins-Smith periodicity theorem in the synthetic setting and show how some of the finite localizations we introduce here can be thought of as a generalization of the full-plane Adams spectral sequence that Mahowald and Rezk introduced for a certain nice class of spectra."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Chromatic homotopy theory in HF_p based synthetic spectra"]}]}],"canonical_facts":{"dc:contributor":["Rezk, Charles W.","Stojanoska, Vesna","Berwick-Evans, Daniel","Heller, Jeremiah"],"dc:creator":["Kundu, Abhra Abir"],"dc:date":["2025-07-17","2025-08"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","The student, Abhra Kundu, accepted the attached license on 2025-07-16 at 16:09.","The student, Abhra Kundu, submitted this Dissertation for approval on 2025-07-16 at 16:22.","This Dissertation was approved for publication on 2025-07-17 at 21:06.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22614 on 2025-10-20 at 16:58:41","In this dissertation, we introduce chromatic homotopy theory in the context of $H\\mathbb{F}_{p}$ based synthetic spectra. Then we study it by relating it to the classical chromatic homotopy theory of spectra and chromatic homotopy theory of its algebraic counterpart. Along the way we prove a version of Hopkins-Smith periodicity theorem in the synthetic setting and show how some of the finite localizations we introduce here can be thought of as a generalization of the full-plane Adams spectral sequence that Mahowald and Rezk introduced for a certain nice class of spectra."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/129886"],"dc:language":["en","eng"],"dc:rights":["Copyright 2025 Abhra Kundu"],"dc:subject":["Homotopy Theory","Synthetic Spectra","Chromatic Homotopy Theory","Algebraic Topology"],"dc:title":["Chromatic homotopy theory in HF_p based synthetic spectra"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:06Z"}