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