Chromatic homotopy theory in HF_p based synthetic spectra
Kundu, Abhra Abir
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https://hdl.handle.net/2142/129886
Description
Title
Chromatic homotopy theory in HF_p based synthetic spectra
Author(s)
Kundu, Abhra Abir
Issue Date
2025-07-17
Director of Research (if dissertation) or Advisor (if thesis)
Rezk, Charles W.
Doctoral Committee Chair(s)
Stojanoska, Vesna
Committee Member(s)
Berwick-Evans, Daniel
Heller, Jeremiah
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Homotopy Theory
Synthetic Spectra
Chromatic Homotopy Theory
Algebraic Topology
Language
eng
Abstract
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.
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