The monochromatic Hahn-Wilson conjecture

TL;DR

This paper proves a significant conjecture in algebraic topology related to fp-spectra and Brown-Peterson spectra, establishing new results at the $K(n)$-local level and confirming the conjecture at height 1.

Contribution

It establishes the $K(n)$-local analogue of the Hahn-Wilson conjecture and demonstrates the generation of fp-spectra by truncated Brown-Peterson spectra.

Findings

Proved the $K(n)$-local Hahn-Wilson conjecture.

Established the generation of fp-spectra by truncated Brown-Peterson spectra.

Constructed $K(n)$-local finite complexes with regular homotopy rings.

Abstract

We prove the $K(n)$-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 $K(n)$-local finite complexes with particularly regular rings of homotopy groups.