Moduli stack of formal group laws

In algebraic geometry, the moduli stack of formal group laws is a stack classifying formal group laws and isomorphisms between them. It is denoted by $$\mathcal{M}_{\text{FG}}$$. It is a "geometric “object" that underlies the chromatic approach to the stable homotopy theory, a branch of algebraic topology.

Currently, it is not known whether $$\mathcal{M}_{\text{FG}}$$ is a derived stack or not. Hence, it is typical to work with stratifications. Let $$\mathcal{M}^n_{\text{FG}}$$ be given so that $$\mathcal{M}^n_{\text{FG}}(R)$$ consists of formal group laws over R of height exactly n. They form a stratification of the moduli stack $$\mathcal{M}_{\text{FG}}$$. $$\operatorname{Spec} \overline{\mathbb{F}_p} \to \mathcal{M}^n_{\text{FG}}$$ is faithfully flat. In fact, $$\mathcal{M}^n_{\text{FG}}$$ is of the form $$\operatorname{Spec} \overline{\mathbb{F}_p} / \operatorname{Aut}(\overline{\mathbb{F}_p}, f)$$ where $$\operatorname{Aut}(\overline{\mathbb{F}_p}, f)$$ is a profinite group called the Morava stabilizer group. The Lubin–Tate theory describes how the strata $$\mathcal{M}^n_{\text{FG}}$$ fit together.