Make script happier

Please ignore this
stacks · Jul 22, 2019 · 272a396 · 272a396
1 parent f4540e2
commit 272a396
Show file tree

Hide file tree

Showing 4 changed files with 4 additions and 9 deletions.
diff --git a/divisors.tex b/divisors.tex
@@ -3332,7 +3332,7 @@ \section{Complements of affine opens}
 \end{proof}
 
 \begin{lemma}
-\label{lemma-generalization-of-complement-open-affine-effective-cartier-divisor}
+\label{lemma-complement-open-affine-effective-cartier-divisor-bis}
 Let $X$ be a Noetherian scheme with affine diagonal. Let $U \subset X$ be
 a dense affine open. If $\mathcal{O}_{X, x}$ is a UFD for all
 $x \in X \setminus U$, then there exists an effective Cartier

diff --git a/intersection.tex b/intersection.tex
@@ -2080,12 +2080,7 @@ \section{Projection formula for flat proper morphisms}
 Thus $V \to Y$ is finite in an open neighbourhood of $\xi$, see
 Cohomology of Schemes, Lemma
 \ref{coherent-lemma-proper-finite-fibre-finite-in-neighbourhood}.
-Using a very general projection formula\footnote{This can be avoided
-by working in an affine neighbourhood of $\xi$ as above, choosing
-an affine open of $X$ containing the generic points of the $Z_i$, and
-translating the question into algebra. Doing this will produce a
-relatively elementary proof of (\ref{equation-stalks}).}
-for derived tensor products, we get
+Using a very general projection formula for derived tensor products, we get
 $$
 Rf_*(\mathcal{O}_V \otimes_{\mathcal{O}_X}^\mathbf{L} Lf^*\mathcal{O}_W) =
 Rf_*\mathcal{O}_V \otimes_{\mathcal{O}_Y}^\mathbf{L} \mathcal{O}_W

diff --git a/perfect.tex b/perfect.tex
@@ -7354,7 +7354,7 @@ \section{The resolution property}
 We may and do assume $U_j$ nonempty for all $j$.
 By More on Algebra, Lemma \ref{more-algebra-lemma-regular-local-UFD}
 the local rings of $X$ are UFDs and hence by Divisors, Lemma
-\ref{divisors-lemma-generalization-of-complement-open-affine-effective-cartier-divisor}
+\ref{divisors-lemma-complement-open-affine-effective-cartier-divisor-bis}
 we can find an effective Cartier divisors $D_j \subset X$
 whose complement is $U_j$. Then the ideal sheaf of $D_j$ is
 invertible, hence a finite locally free module and we conclude

diff --git a/tags/tags b/tags/tags
@@ -18095,7 +18095,7 @@
 0EGG,algebra-example-locally-nilpotent-not-nilpotent
 0EGH,algebra-lemma-uple-generated-degree-1
 0EGI,algebra-lemma-quotient-module-ML
-0EGJ,divisors-lemma-generalization-of-complement-open-affine-effective-cartier-divisor
+0EGJ,divisors-lemma-complement-open-affine-effective-cartier-divisor-bis
 0EGK,varieties-remark-exact-sequence-induction-cohomology
 0EGL,dualizing-remark-matlis
 0EGM,obsolete-section-sites