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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 13th 2013

am splitting-off Lubin-Tate formal group from Lubin-Tate theory

(but as of yet neither entry states the full definition, to be expanded…)

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeNov 13th 2013

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?

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeNov 13th 2013
• (edited Nov 13th 2013)

Hmm, shouldn’t it say $Spec \overline{\mathbb{F}}_{\mathrm{p}_p}$?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeNov 13th 2013

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.

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeNov 13th 2013

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 $n$.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 13th 2013