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.
