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

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)$betweenhomotopycategoriesof$E$-local spectra and differential $E_{\ast }E$-comodules, generalizing Bousfield’s and Franke’s results to heights $n>1$.