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Missing index and prime
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aisejohan committed Apr 4, 2019
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Expand Up @@ -38590,10 +38590,10 @@ \section{\'Etale ring maps}
}
$$
as in said lemma. Since the residue fields at $\mathfrak p$ and $\mathfrak p'$
are the same, the fibre rings of $S/R$ and $(A \times B)/R'$
are the same, the fibre rings of $S/R$ and $(A_1 \times B')/R'$
are the same. Hence, by induction on the number of isolated closed points
of the fibre we may assume that the lemma holds for
$R' \to B$ and $\mathfrak p'$. Thus we get an \'etale ring
$R' \to B'$ and $\mathfrak p'$. Thus we get an \'etale ring
map $R' \to R''$, a prime $\mathfrak p'' \subset R''$ and
a decomposition
$$
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