diff --git a/algebraization.tex b/algebraization.tex index a79ee3d4..2d82a7c7 100644 --- a/algebraization.tex +++ b/algebraization.tex @@ -4081,7 +4081,7 @@ \section{Algebraization of formal sections, II} \begin{proof}[First proof] Recall that $A$ is universally catenary and with Gorenstein -formal fibres, see Local Cohomology, Lemmas +formal fibres, see Dualizing Complexes, Lemmas \ref{dualizing-lemma-dualizing-gorenstein-formal-fibres} and \ref{dualizing-lemma-universally-catenary}. Thus we may consider the map $\mathcal{F} \to \mathcal{F}'$ constructed in diff --git a/more-etale.tex b/more-etale.tex index ad57e9aa..cd0a8326 100644 --- a/more-etale.tex +++ b/more-etale.tex @@ -3507,7 +3507,7 @@ \section{Derived lower shriek via compactifications} \item the isomorphism $g^{-1} \circ Rf_! \to Rf'_! \circ (g')^{-1}$ of Lemma \ref{lemma-base-change-shriek} and the base change map of -Cohomology on Sites, Lemma \ref{sites-cohomology-remark-base-change}. +Cohomology on Sites, Remark \ref{sites-cohomology-remark-base-change}. \end{enumerate} Namely, choose a compactification $j : X \to \overline{X}$ over $Y$ and denote $\overline{f} : \overline{X} \to Y$ the structure morphism. diff --git a/more-morphisms.tex b/more-morphisms.tex index 5fe9d755..bc0cb425 100644 --- a/more-morphisms.tex +++ b/more-morphisms.tex @@ -22335,7 +22335,7 @@ \section{More on weightings} We will also use elementary properties of constructible subsets of schemes and topological spaces, see Topology, Section \ref{topology-section-constructible} and -Properties of Schemes, Section \ref{properties-section-constructible}. +Properties, Section \ref{properties-section-constructible}. Using this the reader sees question is local on $X$ and $Y$; details omitted. Hence we may assume $X$ and $Y$ are affine. If we can find a surjective morphism $Y' \to Y$ diff --git a/obsolete.tex b/obsolete.tex index 7dd2d6e0..5b95d90b 100644 --- a/obsolete.tex +++ b/obsolete.tex @@ -2076,7 +2076,7 @@ \section{Representability in the regular proper case} \end{lemma} \begin{proof} -This follows from Derived Categorie of Varieties, Theorem +This follows from Derived Categories of Varieties, Theorem \ref{equiv-theorem-bondal-van-den-bergh} and Lemma \ref{equiv-lemma-homological-representable}. We also give another proof below.