# Erroneous reference to EGA I 6.9.17 and Deligne's formula

I'm attempting to track down the original EGA proof of Deligne's formula that for a noetherian ring $$A$$, ideal $$\mathfrak{a}\subset A$$, and $$A$$-module $$M$$ we have $$\varinjlim \operatorname{Hom}_A(\mathfrak{a}^n,M) \cong \widetilde{M}\left(\operatorname{Spec} A \setminus V(\mathfrak{a})\right)$$ which I've heard cited as EGA I prop 6.9.17. Unfortunately, the version of EGA hosted by Numdam here (warning, large file) does not even contain a section 6.9. What's going on?

• I know I’m not answering at all the question, but there’s probably a pretty good proof somewhere in stacks project (I remember seeing this somewhere but absolutely not what for). In general, I’d first suggest trying to find the statement in the other EGA at the same number. Mar 3 '21 at 0:08
• I've checked the proof in Stacks (it's 01PM), but I want to read the EGA presentation too. As far as other volumes of EGA, none of those volumes available on Numdam have what I'm looking for as 6.9.17. Mar 3 '21 at 1:08

Proposition (6.9.17) Let $$X$$ be a noetherian scheme, $$\newcommand{\I}{\mathscr{I}} \I$$ a quasicoherent $$\newcommand{\O}{\mathscr{O}} \O_X$$-module, $$Y$$ the closed subscheme of $$X$$ defined by $$\I$$, and $$U$$ the open set $$X \setminus Y$$. Let $$\newcommand{\F}{\mathscr{F}} \F$$ be a coherent $$\O_U$$-module, $$\newcommand{\G}{\mathscr{G}} \G$$ a quasicoherent $$\O_X$$-module, $$\F'$$ a coherent $$\O_X$$-module such that $$\F'|_U = \F$$ (6.9.8). Then we have a canonical bijection $$$$\DeclareMathOperator{\Hom}{Hom} \varinjlim_n \Hom_{\O_X}(\I^n \F', \G) \overset{\sim}{\to} \Hom_{\O_U}(\F, \G|_U) \, . \tag{6.9.17.1}$$$$