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The monochromatic Hahn-Wilson conjecture

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arxiv 2410.08029 v2 pith:YE27BI75 submitted 2024-10-10 math.AT

David Jongwon Lee , Piotr Pstrągowski This is my paper · ORCID
classification math.AT
keywords conjecturefp-spectrahahn-wilsonlocalprovealonganaloguebrown-peterson
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abstract

We prove the $K(n)$-local analogue of the Hahn-Wilson conjecture on fp-spectra, which states that the truncated Brown-Peterson spectra generate the category of fp-spectra as a thick subcategory. As a corollary, we deduce the original conjecture at height $1$. Along the way, we prove the existence of $K(n)$-local finite complexes with particularly regular rings of homotopy groups.

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  1. On higher real $K$-theories and finite spectra

    math.KT 2025-07 conditional novelty 8.0 of 10

    At the prime 2, the connective higher real K-theories eo_h are shown to be fp spectra of type h, which implies a divisibility constraint on Euler characteristics and a new obstruction to generalized Moore spectra.

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