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