The G-actions on the Brauer groups of Lubin-Tate spectra

We show that Hopkins and Lurie’s [1] computation of the Brauer group Br(E) of a Lubin-Tate spectrum E can be used to describe the G-action on Br(E) for G any finite subgroup of the Morava stabilizer group. To do this, we equip their category of synthetic E-modules with a coherent G-action and show that the synthetic analogue functor is symmetric monoidally equivariant. We then show that our G-action on Syn_E induces a G-action on the Hopkins-Lurie filtration of Br(E), giving a filtration of Br(E) as a G-module. Finally, we give an explicit description of the G-action on the Brauer group of the abelian category of Milnor modules, which serves as the bottom of the filtration computing Br(E).

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

• Halladay, Zachary

Contributors dc:contributor

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

• homotopy theory
• Brauer groups
• chromatic homotopy theory
• equivariant homotopy theory

Statement dc:rights

• Copyright 2025 Zachary Halladay

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129452

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129452