Counterexamples to finite generation at chromatic height two

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Refutes the Hahn–Wilson conjecture at chromatic height two. For every sufficiently large prime p, constructs a connective p-complete spectrum of exact fp-type two that cannot be built from completed \(\mathrm{BP}\langle2\rangle\) by finitely many sums, shifts, cones and retracts. The examples nevertheless satisfy the finite and telescopic localization comparisons.

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The paper states

Theorem 1.1

In Counterexamples to the Hahn-Wilson conjecture at height two, 26 September 2026

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For every sufficiently large prime p, there is a connective p-complete spectrum X of exact fp-type two such that, for a standard form of \BP\langle2\rangle_p^\wedge,

X\notin\Thick(\BP\langle2\rangle_p^\wedge).

The same spectrum satisfies

L_2^fX\simeq L_2X, \qquad L_{T(2)}X\simeq L_{K(2)}X.

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Counterexamples to the Hahn-Wilson conjecture at height two

26 September 2026, current edition.

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We disprove the Hahn–Wilson conjecture at height two. For every sufficiently large prime p, we construct a connective p-complete spectrum X of exact fp-type two outside the ordinary thick subcategory generated by the specified standard form of \(\mathrm{BP}\langle2\rangle_p^\wedge\). The same spectrum satisfies both localization comparisons \(L_2^fX\simeq L_2X\) and \(L_{T(2)}X\simeq L_{K(2)}X\).

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Papers elsewhere in the release that this family’s papers cite

Stabilizer orbits and thick tensor ideals of dualizable K(n)-local spectraCurrent edition; no accompanying Lean statement Family The Hovey–Strickland and Chai conjecturesCited by Counterexamples to the Hahn-Wilson conjecture at height two.

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31 references in Counterexamples to the Hahn-Wilson conjecture at height two

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An unsigned public tier list, the OpenAI Math Tier List, classes it as a counterexample and rates its significance, if it holds up, as “Solid publication, could lead to tenure”. The page says that nothing on it is verified.
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