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I am trying to understand proposition 3.6 of this paper (perhaps I am in over my head):

https://arxiv.org/pdf/math/0703310.pdf

If we denote the stack $\mathcal{M}$ and its coarse moduli space as $M$ then in the first couple of lines of the proof it is written that:

"By standard limit arguments we may assume that $M$ is the spectrum of a local henselian ring $R$ with residue field $k$".

My question is: I have seen what is more or less this same line written in many proofs of different flavors of the above proposition. What are these standard limit arguments and where can I find references for them?

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    $\begingroup$ When I write "standard limit arguments" in my own papers, I usually mean: EGA IV_3, Section 8, Sections 11.2 -- 11.3, EGA IV_4, Section 17.7, and maybe Section 19.8. $\endgroup$
    – Jason Starr
    Commented Jan 12, 2017 at 13:25
  • $\begingroup$ Thank you Jason, I just briefly skimmed these sections and they look useful :). $\endgroup$
    – Fred
    Commented Jan 12, 2017 at 13:42

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