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Fix typos in statement 0AN8
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aisejohan committed May 5, 2016
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6 changes: 3 additions & 3 deletions formal-spaces.tex
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Expand Up @@ -3276,16 +3276,16 @@ \section{Morphisms representable by algebraic spaces}
\begin{enumerate}
\item $Y$ is McQuillan, i.e., equal to $\text{Spf}(B)$ for some
weakly admissible topological $S$-algebra $B$, and
\item $f : Y \to X$ is representable by algebraic spaces and \'etale.
\item $f : X \to Y$ is representable by algebraic spaces and \'etale.
\end{enumerate}
Then there exists an \'etale ring map $B \to A$ such that
$$
Y = \text{Spf}(A^\wedge)
X = \text{Spf}(A^\wedge)
\quad\text{where}\quad
A^\wedge = \lim A/JA
$$
with $J \subset B$ running over the weak ideals of definition of $B$.
In particular, $Y$ is McQuillan.
In particular, $X$ is McQuillan.
\end{lemma}

\begin{proof}
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