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am splitting-off Lubin-Tate formal group from Lubin-Tate theory
(but as of yet neither entry states the full definition, to be expanded…)
Not that I understand, but in
The stratum $\mathcal{M}_{FG}^n$ can be identified with the homotopy quotient $\overline{\mathbb{F}}_{\mathrm{p}_p}// \mathbb{G}$, where the group $\mathbb{G}$ is the Morava stabilizer group. (Lurie 10, lect. 19)
where’s the dependence on $n$ in $\overline{\mathbb{F}}_{\mathrm{p}_p}// \mathbb{G}$, and what is that second $p$ subscript anyway.
And did you mean lecture 19, when it’s 21 that you get sent to?
Hmm, shouldn’t it say $Spec \overline{\mathbb{F}}_{\mathrm{p}_p}$?
Thanks for catching this. I have now fixed it to read as follows:
Write $\overline{\mathbb{F}_{\mathrm{p}}}$ for the algebraic closure of $\mathbb{F}_p$.
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 Morava stabilizer group.
This is (Lurie 10, lect. 19, prop. 1) See also the beginning of Lurie 10, lect 21.
You changed it at Morava stabilizer group, but it has it the old way at Lubin-Tate+theory. Did you want that repetition between the pages?
Anyway, somewhere it should point out that $\mathbb{G} = Aut(\overline{\mathbb{F}}_{\mathrm{p}}, f)$, so I’ve added that to Morava stabilizer group. Should I now copy all that over to Lubin-Tate+theory?
Oh, so the dependence on $n$ comes in through the height of $f$, the unique formal group law of that height $n$.
Thanks for adding!
Right, we don’t need not say this at “Lubi-Tate theory” (and should not, since there it’s a distraction, at least in the Idea section), have removed it there.
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