# User:TakuyaMurata/Moduli stack of formal group laws

In algebraic geometry, the **moduli stack of formal group laws** classifies formal group laws and isomorphisms between them. It is denoted by . It is a "geometric “object" that underlies the chromatic approach to the stable homotopy theory, a branch of algebraic topology. This moduli stack is closely related to the moduli stack of elliptic curves.Template:Vague

In characteristic zero, this moduli stack is very easy to understand: the quotient stack is isomorphic to , the classifying stack. This can be thought of as a manifestation of the "thesis" of differential graded Lie algebras.

Currently, it is not known whether is a derived stack or not. Hence, it is typical to work with stratifications. Let be given so that consists of formal group laws over *R* of height exactly *n*. They form a stratification of the moduli stack . is faithfully flat. In fact, is of the form where is a profinite group called the **Morava stabilizer group**. The Lubin–Tate theory describes how the strata fit together.

## Moduli stack of *p*-divisible groups

- See also
*p*-divisible groups.

## References

- J. Lurie, Chromatic Homotopy Theory (252x)
- P. Goerss, Realizing families of Landweber exact homology theories