Chromatic homotopy is algebraic when $p > n^{2}+n+1$

TL;DR

This paper proves that for certain $p$-local Landweber exact homology theories with sufficiently large primes, the homotopy category of $E$-local spectra is algebraically equivalent to the derived category of $E_*E$-comodules, extending previous results.

Contribution

It establishes an algebraic model for the homotopy category of $E$-local spectra at heights greater than one when $p > n^2 + n + 1$, generalizing earlier work.

Findings

Homotopy categories are equivalent to derived categories of comodules.

The equivalence holds for primes larger than $n^2 + n + 1$.

Extends algebraic models to higher heights.

Abstract

We show that if $E$ is a $p$-local Landweber exact homology theory of height $n$ and $p > n^2+n+1$, then there exists an equivalence $h \mathcal{S}p_{E} \simeq h\mathcal{D}(E_{*}E)$ between homotopy categories of $E$-local spectra and differential $E_{*}E$-comodules, generalizing Bousfield's and Franke's results to heights $n > 1$.