User:TakuyaMurata/Moduli stack of formal group laws

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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.


Further reading

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