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.

Manuscript

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

September 24, 2026 · source · cite as \cite{OAI:Stabilizer-Orbits-and-Thick-Tensor-Ideals-of-Dualizable-Kn-Local-Spectra-September-24-2026}

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.

Result 311 · Topology. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.