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Fix typos in divisors

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aisejohan committed Sep 10, 2018
1 parent 9a7776c commit 8b7d3bdfda6d612220d7e9bd8ffd592b041ab69f
Showing with 2 additions and 2 deletions.
  1. +2 −2 divisors.tex
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@@ -7173,8 +7173,8 @@ \section{Weil divisors on normal schemes}
$$
1 = \sum f_i g_i
$$
for some $n > 0$, $f_i \in \mathfrak m_x$, and $g_i \in \mathcal{O}(U_x)$.
By induction on $d$ we know that $D(f_i) \cap U_x$ is affine
for some $n > 0$, $f_i \in \mathfrak m_x$, and $g_i \in \mathcal{O}(U)$.
By induction on $d$ we know that $D(f_i) \cap U$ is affine
for all $i$: going through the whole argument just given with
$X$ replaced by $D(f_i)$ we end up with Noetherian local rings
whose dimension is strictly smaller than $d$. Hence $U$

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