Counterexamples to finite generation at chromatic height two
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
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 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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MANUSCRIPT 01
Counterexamples to the Hahn-Wilson conjecture at height two
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 BP\langle2\rangle_p^\wedge. The same spectrum satisfies both localization comparisons…
Full source abstract
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 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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