The Hovey-Strickland conjecture: the thick tensor ideals of dualizable K(n)-local spectra

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

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

VibeMathed record: The Hovey-Strickland conjecture: the thick tensor ideals of dualizable K(n)-local spectra evidence for this event

Hovey-Strickland, Morava K-theories and localisation (Mem. AMS 1999) evidence for this event

Theorem 1.2: for every prime $p$ and $n\ge1$ the thick tensor ideals of the dualizable $K(n)$-local category are exactly $\mathcal D_0\supsetneq\cdots\supsetneq\mathcal D_n\supsetneq\mathcal D_{n+1}=0$, so there are $n+2$ of them and each $\mathcal D_k$ does not depend on the chosen type-$k$ spectrum; a corollary identifies the Balmer spectrum with the $n+1$ proper members of the chain, with its specialization order. It is deduced from Theorem 1.1 (Chai's conjecture, a separate entry) by the known Barthel-Heard-Naumann implication. It concerns dualizable objects only and does not classify localizing or other subcategories of the whole $K(n)$-local category. Height two was already known. parent of this event

The Hovey-Strickland conjecture: the thick tensor ideals of dualizable K(n)-local spectra parent of this event