Level 1: Finite generation for the K(n)-local sphere

A
D
V
E
R
T

I
S
E
M
E
N
T

LEVEL 1 OF 1 · Finite generation for the $K(n)$-local sphere

Finite generation for the K(n)-local sphere

expertly designed by an internal OpenAI model · released 2026-09-24 · original PDF

LEVEL FAILED TO LOAD

We couldn't convert this paper's source. You can still play it as a PDF.

How to play: 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.

Back to game page

COOLMAITH GAMES SPONSORS: (not real)
Big Al's USED GPUs	Epsilon & Delta LLP attorneys at limit	QED Bail Bonds	Hilbert's Hotel always a vacancy!

Cool Links: openai/math Lean Mathlib arXiv the real Coolmath Games

You are visitor number 000719

Thanks for visiting CoolmAIth Games
© 1997-2026 CoolmAIth Games. A parody. Not affiliated with Coolmath.com LLC or OpenAI.
Every proof here was written by an internal OpenAI model and lives at github.com/openai/math.
Best viewed in Netscape Navigator 4.0 at 800x600