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

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Topology

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