Topology·OpenAI Math·Result 313
Finite generation for the K(n)-local sphere
One of the 372 results in OpenAI's public mathematics catalogue, filed under topology: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Finite generation for the K(n)-local sphere
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What OpenAI claims
Answers the degreewise finiteness question of Hovey and Hovey–Strickland: every homotopy group of the K(n)-local sphere is a finitely generated ℤp-module, for every prime, positive height and integer degree. The same conclusion holds after K(n)-localizing any finite p-local spectrum.
Paper
Finite generation for the K(n)-local sphere
We prove that the homotopy groups of the K(n)-local sphere are finitely generated ℤp-modules in every integer degree, for every prime p and positive height n. Equivalently, the same conclusion holds after K(n)-localizing any finite p-local spectrum. This answers the degreewise finiteness question of Hovey and Hovey–Strickland.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
