2026-09-23T06:52:09Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/129886 2025-10-25 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

application/pdf en text 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 Chromatic homotopy theory in HF_p based synthetic spectra Kundu, Abhra Abir 2025-07-17 Rezk, Charles W. Stojanoska, Vesna Berwick-Evans, Daniel Heller, Jeremiah Homotopy Theory Synthetic Spectra Chromatic Homotopy Theory Algebraic Topology eng 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. 2025-08 Text https://hdl.handle.net/2142/129886 Copyright 2025 Abhra Kundu Mathematics Mathematics University of Illinois Urbana-Champaign Ph.D. Dissertation