# Contents

## Idea

The moduli stack of formal groups $\mathcal{M}_{FG}$ (1-dimensional commutative formal groups) admits a natural stratification whose open strata are labeled by a natural number called the height of formal groups.

For $p$ a prime number, write $\overline{\mathbb{F}}_{\mathrm{p}}$ for the algebraic closure of the prime field $\mathbb{F}_p$.

The stratum $\mathcal{M}_{FG}^n$ can be identified with the homotopy quotient $Spec (\overline{\mathbb{F}}_{\mathrm{p}})// \mathbb{G}$, where the group $\mathbb{G}$ is the automorphism group over $\mathbb{F}_p$ of the unique formal group law $f$ of height $n$,

$\mathbb{G} \coloneqq Aut(\overline{\mathbb{F}}_{\mathrm{p}}, f)$

This is called the Morava stabilizer group. Essentially its group algebra (Hopf algebra) is called the Morava stabilizer algebra.

This is discussed around (Lurie 10, lect. 19, prop. 1), see also the beginning of Lurie 10, lect 21, and in (Ravenel, chapt. 6).

The deformation theory around these strata is Lubin-Tate theory.

## References

Last revised on February 5, 2016 at 16:16:35. See the history of this page for a list of all contributions to it.