Ravenel's Local-Global Conjecture for formal module Ext groups

Let $K/\mathbb{Q}$ be a finite field extension with ring of integers $A$. For a prime ideal $\mathfrak{p}$ of $A$, write $A_{\mathfrak{p}}$ for the localization of $A$ at $\mathfrak{p}$. Let $L^A,L^AB$ be the classifying Hopf algebroid for one-dimensional formal $A$-modules and let $V^{A_{\mathfrak{p}}},V^{A_{\mathfrak{p}}}T$ be the classifying Hopf algebroid for $A_{\mathfrak{p}}$-typical one-dimensional formal modules. For every $s,t$, every prime ideal $\mathfrak{p}$, and every graded $(L^A,L^AB)$-comodule $M$, Ravenel's Local-Global Conjecture. There exists an isomorphism of $A_{\mathfrak{p}}$-modules

$$A_{\mathfrak{p}} \otimes_A \operatorname{Ext}_{(L^A,L^AB)}^{s,t}(L^A,M) \cong \operatorname{Ext}_{(V^{A_{\mathfrak{p}}},V^{A_{\mathfrak{p}}}T)}^{s,t}(V^{A_{\mathfrak{p}}},V^{A_{\mathfrak{p}}}\otimes_{L^{A_{\mathfrak{p}}}}M).$$

This asserts compatibility between global and local computations of Ext groups for formal $A$-modules. The conjecture was proven in full generality by A. Pearlman using Cartier typicalization and a Hopf algebroid change-of-rings argument.