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dc.contributor.advisorHahn, Jeremy
dc.contributor.authorLee, David Jongwon
dc.date.accessioned2025-07-07T17:39:08Z
dc.date.available2025-07-07T17:39:08Z
dc.date.issued2025-05
dc.date.submitted2025-05-13T13:31:21.694Z
dc.identifier.urihttps://hdl.handle.net/1721.1/159928
dc.description.abstractWhen p is an odd prime, we prove that the Fp-cohomology of BP⟨n⟩ as a module over the Steenrod algebra determines the p-local spectrum BP⟨n⟩. In particular, we prove that the p-local spectrum BP⟨n⟩ only depends on its p-completion BP⟨n⟩p̂. As a corollary, this proves that the p-local homotopy type of BP⟨n⟩ does not depend on the ideal by which we take the quotient of BP. In the course of the argument, we show that there is a vanishing line for odd degree classes in the Adams spectral sequence for endomorphisms of BP⟨n⟩. We also prove that there are enough endomorphisms of BP⟨n⟩ in a suitable sense. When p = 2, we obtain the results for n ≤ 3.
dc.publisherMassachusetts Institute of Technology
dc.rightsIn Copyright - Educational Use Permitted
dc.rightsCopyright retained by author(s)
dc.rights.urihttps://rightsstatements.org/page/InC-EDU/1.0/
dc.titleUniqueness of p-local truncated Brown-Peterson spectra
dc.typeThesis
dc.description.degreePh.D.
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
mit.thesis.degreeDoctoral
thesis.degree.nameDoctor of Philosophy


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