The monochromatic Hahn-Wilson conjecture

Abstract We prove the $K(n)$ K ( n ) -local analogue of the Hahn-Wilson conjecture on fp-spectra, which states that the truncated Brown-Peterson spectra generate the category of fp-spectra as a thick subcategory. As a corollary, we deduce the original conjecture at height 1. Along the way, we prove the existence of $K(n)$ K ( n ) -local finite complexes with particularly regular rings of homotopy groups.