Uniqueness of p-local truncated Brown-Peterson spectra
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lee-jongwonl-phd-math-2025-thesis.pdf
Description
Thesis PDF
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554.68 KB
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Author(s)
Lee, David Jongwon
Advisor(s)
Hahn, Jeremy
Date Issued
May 2025
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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