TITLE: Erroneous reference to EGA I 6.9.17 and Deligne's formula
QUESTION [5 upvotes]: 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?

REPLY [5 votes]: I think they are citing the 1971 edition of EGA I published by Springer.
Grothendieck, Alexandre; Dieudonné, Jean (1971). Éléments de géométrie algébrique: I. Le langage des schémas. Grundlehren der Mathematischen Wissenschaften (in French). 166 (2nd ed.). Berlin; New York: Springer-Verlag. ISBN 978-3-540-05113-8.
In this edition, Proposition 6.9.17 is the following (my translation).
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
\begin{equation}
\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}
\end{equation}