Counterexamples to finite generation at chromatic height two

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.

Manuscript

Counterexamples to the Hahn-Wilson conjecture at height two

September 26, 2026 · source · cite as \cite{OAI:Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026}

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.

Result 319 · Topology. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.