Invariant Primes in Lubin-Tate Space and Hovey-Strickland at Every Height
Abstract
Let Hn be the one-dimensional Honda formal group of height n over Fpn and let Rn=W(Fpn)[[u1,…,un−1]], An=Rn/(p). We prove, for every height n and every prime p, that the prime ideals of An stable under an open subgroup of the Morava stabilizer group are exactly the height ideals (u1,…,uj). We also prove that a stable prime of Rn avoiding p is zero. The resulting radical-ideal classification implies the Hovey-Strickland classification of thick tensor ideals in the category of dualizable K(n)-local spectra via the forward implication of Barthel-Heard-Naumann. The special-fiber argument is local and geometric. After cutting an invariant prime by a one-parameter curve, we construct from the Cartier structure equation a smooth formal quotient 𝒬 and a distinguished subgroup ℋ. The generic fiber of ℋ is identified with the deformation space of connected-étale extensions. A Cartier obstruction map from the full Honda endomorphism order is compared with evaluation on Tate vectors through completed universal covers. Fargues-Fontaine vector bundles give a period-detection statement. Chai's rigidity theorem then promotes detection by homomorphisms to formal Zariski density after a renormalization of the valuation. A uniform fixed-jet argument transfers this density to Morava-stabilizer orbits. The generic-fiber assertion is proved separately from the Gross-Hopkins period map.
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BibTeX
@misc{ma2026invariant,
title = {{Invariant Primes in Lubin-Tate Space and Hovey-Strickland at Every Height}},
author = {Chenglong Ma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10072},
eprint = {2610.10072},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10072},
}
RIS
TY - UNPB
TI - Invariant Primes in Lubin-Tate Space and Hovey-Strickland at Every Height
AU - Chenglong Ma
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10072
UR - https://arxiv.org/abs/2610.10072
AB - Let H_n be the one-dimensional Honda formal group of height n over F_p^n and let R_n=W(F_p^n)[[u_1,…,u_n−1]], A_n=R_n/(p). We prove, for every height n and every prime p, that the prime ideals of A_n stable under an open subgroup of the Morava stabilizer group are exactly the height ideals (u_1,…,u_j). We also prove that a stable prime of R_n avoiding p is zero. The resulting radical-ideal classification implies the Hovey-Strickland classification of thick tensor ideals in the category of dualizable K(n)-local spectra via the forward implication of Barthel-Heard-Naumann. The special-fiber argument is local and geometric. After cutting an invariant prime by a one-parameter curve, we construct from the Cartier structure equation a smooth formal quotient 𝒬 and a distinguished subgroup ℋ. The generic fiber of ℋ is identified with the deformation space of connected-étale extensions. A Cartier obstruction map from the full Honda endomorphism order is compared with evaluation on Tate vectors through completed universal covers. Fargues-Fontaine vector bundles give a period-detection statement. Chai's rigidity theorem then promotes detection by homomorphisms to formal Zariski density after a renormalization of the valuation. A uniform fixed-jet argument transfers this density to Morava-stabilizer orbits. The generic-fiber assertion is proved separately from the Gross-Hopkins period map.
ER -