dc.contributor.advisor | Hahn, Jeremy | |
dc.contributor.author | Lee, David Jongwon | |
dc.date.accessioned | 2025-07-07T17:39:08Z | |
dc.date.available | 2025-07-07T17:39:08Z | |
dc.date.issued | 2025-05 | |
dc.date.submitted | 2025-05-13T13:31:21.694Z | |
dc.identifier.uri | https://hdl.handle.net/1721.1/159928 | |
dc.description.abstract | When 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.publisher | Massachusetts Institute of Technology | |
dc.rights | In Copyright - Educational Use Permitted | |
dc.rights | Copyright retained by author(s) | |
dc.rights.uri | https://rightsstatements.org/page/InC-EDU/1.0/ | |
dc.title | Uniqueness of p-local truncated Brown-Peterson spectra | |
dc.type | Thesis | |
dc.description.degree | Ph.D. | |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
mit.thesis.degree | Doctoral | |
thesis.degree.name | Doctor of Philosophy | |