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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 FG n\mathcal{M}_{FG}^n can be identified with the homotopy quotient 𝔽¯ p p//𝔾\overline{\mathbb{F}}_{\mathrm{p}_p}// \mathbb{G}, where the group 𝔾\mathbb{G} is the Morava stabilizer group. (Lurie 10, lect. 19)

    where’s the dependence on nn in 𝔽¯ p p//𝔾\overline{\mathbb{F}}_{\mathrm{p}_p}// \mathbb{G}, and what is that second pp 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 Spec𝔽¯ p pSpec \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 𝔽 p¯\overline{\mathbb{F}_{\mathrm{p}}} for the algebraic closure of 𝔽 p\mathbb{F}_p.

    The stratum FG n\mathcal{M}_{FG}^n can be identified with the homotopy quotient Spec(𝔽¯ p)//𝔾Spec (\overline{\mathbb{F}}_{\mathrm{p}})// \mathbb{G}, where the group 𝔾\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 𝔾=Aut(𝔽¯ p,f)\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 nn comes in through the height of ff, the unique formal group law of that height nn.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 13th 2013

    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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