{"id":"openai-math/Finite-generation-for-the-Kn-local-sphere","pdf":"https://github.com/openai/math/blob/main/preprints/Finite-generation-for-the-Kn-local-sphere-September-24-2026/Finite-generation-for-the-Kn-local-sphere-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Finite-generation-for-the-Kn-local-sphere-September-24-2026","tags":["chromatic-homotopy","k-local-sphere","homotopy-groups"],"score":0,"title":"Finite generation for the K(n)-local sphere","domain":"Topology","family":"313","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Finite generation for the $`K(n)`$-local sphere"}