OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
Answers the degreewise finiteness question of Hovey and Hovey–Strickland: every homotopy group of the K(n)-local sphere is a finitely generated ℤ_(p)-module, for every prime, positive height and integer degree. The same conclusion holds after K(n)-localizing any finite p-local spectrum.
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MANUSCRIPT 01
Finite generation for the K(n)-local sphere
We prove that the homotopy groups of the K(n)-local sphere are finitely generated ℤ_(p)-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…
Full source abstract
We prove that the homotopy groups of the K(n)-local sphere are finitely generated ℤ_(p)-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.
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New mathematical reasoning could help AI tackle harder scientific and computational problems. How reliably these skills transfer beyond mathematics will determine how much they contribute to general intelligence.