Source authenticated

Chai's conjecture on stabilizer-invariant ideals of the Lubin-Tate deformation ring

Theorem 1.1: for any open subgroup $U\subseteq A_n^\times$ , the proper $U$ -stable primes of $E_0$ are exactly $0,I_1,\ldots,I_n$ and the $U$ -invariant radical ideals are exactly $0,I_1,\ldots,I_n,E_0$ ; the radical ideals invariant under the full extended group $G_n$ are the same list. This is Chai's Hope in the finite-residue-field formulation, at every prime and height, extended to open subgroups. Through Barthel-Heard-Naumann it yields the Hovey-Strickland conjecture (separate entry). It is stated for the Honda formal group over finite-field coefficients and does not treat other residue fields or the full scope of Chai's closed-fiber questions.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Chai's conjecture on stabilizer-invariant ideals of the Lubin-Tate deformation ring · Chai's invariant-ideal conjecture

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Chai's conjecture on stabilizer-invariant ideals of the Lubin-Tate deformation ring

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the introduction and Theorem 1.1 were read against Chai's question and the Barthel-Heard-Naumann formulation (Hope 4.1 and Remark 4.2) as the manuscript cites them. No Lean formalization exists for this family. The manuscript says it proves the standard finite-residue-field formulation and extends it from the full stabilizer to every open subgroup; the core is a local orbit-density theorem at characteristic-p points of height between 1 and n-1, using perfectoid methods, Le Bras's theorem on Banach-Colmez sheaves and the Fargues-Fontaine curve. Chai's unpublished characteristic-zero result and the Gross-Hopkins period map handle primes not containing p. Not refereed here.

Source ↗

Chai's conjecture on stabilizer-invariant ideals of the Lubin-Tate deformation ring

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Barthel-Heard-Naumann, On conjectures of Hovey-Strickland and Chai (Selecta Math. 2022)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Chai, The group action on the closed fiber of the Lubin-Tate moduli space (Duke 1996)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Lineage and corrections

Barthel-Heard-Naumann, On conjectures of Hovey-Strickland and Chai (Selecta Math. 2022) evidence for this event

This event attributed to Unreleased internal OpenAI model

Chai's conjecture on stabilizer-invariant ideals of the Lubin-Tate deformation ring parent of this event

Chai's conjecture on stabilizer-invariant ideals of the Lubin-Tate deformation ring evidence for this event

VibeMathed record: Chai's conjecture on stabilizer-invariant ideals of the Lubin-Tate deformation ring evidence for this event

Chai, The group action on the closed fiber of the Lubin-Tate moduli space (Duke 1996) evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verify Open canonical problem Explore evidence graph