Chromatic homotopy theory in HF_p based synthetic spectra

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Kundu, Abhra Abir

Contributors dc:contributor

• Rezk, Charles W.
• Stojanoska, Vesna
• Berwick-Evans, Daniel
• Heller, Jeremiah

• Homotopy Theory
• Synthetic Spectra
• Chromatic Homotopy Theory
• Algebraic Topology

Statement dc:rights

• Copyright 2025 Abhra Kundu

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129886

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129886