Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 313-01. Finite generation for the K(n)-local sphere
Manuscript map · lines 8535–8544
OpenAI@2026-10-07#rem:oai-p-313-01
Authors: OpenAI. Family 313.
Title: Finite generation for the K(n)-local sphere.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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