2026-09-23T02:38:05Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/129452 2025-10-20 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 2025-10-19 without embargo terms The student, Zachary Halladay, accepted the attached license on 2025-04-25 at 16:49. The student, Zachary Halladay, submitted this Dissertation for approval on 2025-04-25 at 16:58. This Dissertation was approved for publication on 2025-04-28 at 12:41. DSpace SAF Submission Ingestion Package generated from Vireo submission #21993 on 2025-10-19 at 18:19:21 The G-actions on the Brauer groups of Lubin-Tate spectra Halladay, Zachary 2025-04-28 Stojanoska, Vesna Rezk, Charles Berwick-Evans, Daniel Heller, Jeremiah homotopy theory Brauer groups chromatic homotopy theory equivariant homotopy theory eng 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). 2025-05 Thesis https://hdl.handle.net/2142/129452 Copyright 2025 Zachary Halladay Mathematics Mathematics University of Illinois Urbana-Champaign Ph.D. Dissertation