The G-actions on the Brauer groups of Lubin-Tate spectra
Halladay, Zachary
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https://hdl.handle.net/2142/129452
Description
Title
The G-actions on the Brauer groups of Lubin-Tate spectra
Author(s)
Halladay, Zachary
Issue Date
2025-04-28
Director of Research (if dissertation) or Advisor (if thesis)
Stojanoska, Vesna
Doctoral Committee Chair(s)
Rezk, Charles
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
Brauer groups
chromatic homotopy theory
equivariant homotopy theory
Language
eng
Abstract
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).
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