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Stabilizer orbits and thick tensor ideals of dualizable K(n)-local spectra

OpenAI · September 24, 2026

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Abstract

We classify the prime and radical ideals of the Lubin–Tate deformation ring invariant under an open Morava stabilizer subgroup, at every prime and positive height. This proves Chai's invariant-ideal conjecture in the standard finite-residue-field formulation. It also proves the Hovey–Strickland conjecture: the dualizable $K(n)$-local category has exactly $n+2$ thick tensor ideals, and its Balmer spectrum is a chain of $n+1$ points.

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Follow-up works

  • Chenglong Ma, Invariant Primes in Lubin–Tate Space and Hovey–Strickland at Every Height (arXiv:2610.10072v1, 7 Oct 2026). Proves the same classification of open-stabilizer-stable primes and radical ideals of the Lubin–Tate ring, and the Hovey–Strickland classification via Barthel–Heard–Naumann, by a Cartier-theoretic special-fiber argument; its introduction cites this paper as [8] and says its proof strategy and notation are "identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026". It also reports that Ningyi Li independently proved the same result by a different method, and the HTML version discloses AI assistance with the fixed-jet argument in Appendix A.

Comments and discussion

Possibly relevant literature (found by the agent, not checked)

  • Peter Scholze and Jared Weinstein, Moduli of p-divisible groups (arXiv:1211.6357, 2012/2013). Treats Rapoport–Zink spaces at infinite level (including Lubin–Tate) via universal covers and p-adic Hodge theory, which may bear on the paper's universal-cover comparison of étale Tate vectors with points of the perfected Honda group; Ma's paper cites it, but this paper's bibliography does not.

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Elsewhere

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Cite

@misc{OAI:Stabilizer-Orbits-and-Thick-Tensor-Ideals-of-Dualizable-Kn-Local-Spectra-September-24-2026,
  author = {{OpenAI}},
  title = {{Stabilizer orbits and thick tensor ideals of dualizable $K(n)$-local spectra}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Stabilizer-Orbits-and-Thick-Tensor-Ideals-of-Dualizable-Kn-Local-Spectra-September-24-2026/paper.pdf}{OAI:Stabilizer-Orbits-and-Thick-Tensor-Ideals-of-Dualizable-Kn-Local-Spectra-September-24-2026}},
  year = {2026}
}

Family 311: The Hovey–Strickland and Chai conjectures

Proves Chai's invariant-ideal conjecture for Lubin–Tate deformation rings over finite residue fields, at every prime and positive height n. Through the implication of Barthel–Heard–Naumann, this proves the Hovey–Strickland conjecture: dualizable $K(n)$-local spectra have exactly $n+2$ thick tensor ideals, and their Balmer spectrum is a chain of $n+1$ points.

This is the only paper in this family.