Normalize math commands

We may want to introduce \SheafEnd at a later stage but for the moment
it seems we don't use it a whole lot

etale-cohomology.tex

@@ -8411,10 +8411,10 @@ \section{The Brauer group of a scheme}
 which have positive rank at every $s \in S$ such that
 $$
 \mathcal{A} \otimes_{\mathcal{O}_S}
-\mathcal{E}\!{\it nd}_{\mathcal{O}_S}(\mathcal{F})
+\SheafHom_{\mathcal{O}_S}(\mathcal{F}, \mathcal{F})
 \cong
 \mathcal{B} \otimes_{\mathcal{O}_S}
-\mathcal{E}\!{\it nd}_{\mathcal{O}_S}(\mathcal{G})
+\SheafHom_{\mathcal{O}_S}(\mathcal{G}, \mathcal{G})
 $$
 as $\mathcal{O}_S$-algebras. The {\it Brauer group} of
 $S$ is the set $\text{Br}(S)$ of equivalence classes of Azumaya
@@ -8426,8 +8426,8 @@ \section{The Brauer group of a scheme}
 Let $S$ be a scheme. Let $\mathcal{F}$ and $\mathcal{G}$ be finite locally
 free sheaves of $\mathcal{O}_S$-modules of positive rank. If there
 exists an isomorphism
-$\mathcal{E}\!{\it nd}_{\mathcal{O}_S}(\mathcal{F}) \cong
-\mathcal{E}\!{\it nd}_{\mathcal{O}_S}(\mathcal{G})$ of
+$\SheafHom_{\mathcal{O}_S}(\mathcal{F}, \mathcal{F}) \cong
+\SheafHom_{\mathcal{O}_S}(\mathcal{G}, \mathcal{G})$ of
 $\mathcal{O}_S$-algebras, then there exists an invertible sheaf
 $\mathcal{L}$ on $S$ such that
 $\mathcal{F} \otimes_{\mathcal{O}_S} \mathcal{L} \cong \mathcal{G}$
@@ -8437,8 +8437,8 @@ \section{The Brauer group of a scheme}
 
 \begin{proof}
 Fix an isomorphism
-$\mathcal{E}\!{\it nd}_{\mathcal{O}_S}(\mathcal{F}) \to
-\mathcal{E}\!{\it nd}_{\mathcal{O}_S}(\mathcal{F})$.
+$\SheafHom_{\mathcal{O}_S}(\mathcal{F}, \mathcal{F}) \to
+\SheafHom_{\mathcal{O}_S}(\mathcal{G}, \mathcal{G})$.
 Consider the sheaf $\mathcal{L} \subset \SheafHom(\mathcal{F}, \mathcal{G})$
 generated as an $\mathcal{O}_S$-module by the local isomorphisms
 $\varphi : \mathcal{F} \to \mathcal{G}$ such that conjugation by
@@ -8468,7 +8468,7 @@ \section{The Brauer group of a scheme}
 
 \begin{proof}
 Choose an \'etale covering $\{U_i \to S\}$ and choose isomorphisms
-$\mathcal{A}|_{U_i} \to \mathcal{E}\!{\it nd}(\mathcal{F}_i)$
+$\mathcal{A}|_{U_i} \to \SheafHom(\mathcal{F}_i, \mathcal{F}_i)$
 for some locally free $\mathcal{O}_{U_i}$-modules $\mathcal{F}_i$
 of rank $d$. (We may assume $\mathcal{F}_i$ is free.) Consider the
 composition
@@ -8482,11 +8482,11 @@ \section{The Brauer group of a scheme}
 according to the sign character under the action of the symmetric group
 on $d$ letters. Then $p_i^2 = p_i$ and the rank of $p_i$ is $1$.
 Using the given isomorphism
-$\mathcal{A}|_{U_i} \to \mathcal{E}\!{\it nd}(\mathcal{F}_i)$
+$\mathcal{A}|_{U_i} \to \SheafHom(\mathcal{F}_i, \mathcal{F}_i)$
 and the canonical isomorphism
 $$
-\mathcal{E}\!{\it nd}(\mathcal{F}_i)^{\otimes d} =
-\mathcal{E}\!{\it nd}(\mathcal{F}_i^{\otimes d})
+\SheafHom(\mathcal{F}_i, \mathcal{F}_i)^{\otimes d} =
+\SheafHom(\mathcal{F}_i^{\otimes d}, \mathcal{F}_i^{\otimes d})
 $$
 we may think of $p_i$ as a section of $\mathcal{A}^{\otimes d}$
 over $U_i$. We claim that $p_i|_{U_i \times_S U_j} = p_j|_{U_i \times_S U_j}$
@@ -8509,7 +8509,7 @@ \section{The Brauer group of a scheme}
 $$
 is a locally free module of rank $d^d$ and that (left) multiplication
 by $\mathcal{A}^{\otimes d}$ induces an isomorphism
-$\mathcal{A}^{\otimes d} \to \mathcal{E}\!{\it nd}(\mathcal{H})$.
+$\mathcal{A}^{\otimes d} \to \SheafHom(\mathcal{H}, \mathcal{H})$.
 In other words, $\mathcal{A}^{\otimes d}$ is the trivial element
 of the Brauer group of $S$ as desired.
 \end{proof}

formal-spaces.tex

@@ -752,7 +752,7 @@ \section{Topological rings and modules}
 systems of open submodules in $M$ and $N$.
 The {\it completed tensor product}
 $$
-M \widehat\otimes_R N =
+M \widehat{\otimes}_R N =
 \lim M \otimes_R N/(M_\mu \otimes_R N + M \otimes_R N_\nu) =
 \lim M/M_\mu \otimes_R N/N_\nu
 $$
@@ -765,7 +765,7 @@ \section{Topological rings and modules}
 If $R \to A$ and $R \to B$ are continuous maps of
 linearly topologized rings, then the construction above
 gives a tensor product $A \otimes_R B$ and a completed
-tensor product $A \widehat\otimes_R B$.
+tensor product $A \widehat{\otimes}_R B$.
 
 \medskip\noindent
 We record here the notions introduced in Remark \ref{remark-mcquillan}.
@@ -856,7 +856,7 @@ \section{Topological rings and modules}
 \label{lemma-closure-image-ideal}
 Let $A \to B$ be a continuous map of linearly topologized rings.
 Let $I \subset A$ be an ideal. The closure of $IB$
-is the kernel of $B \to B \widehat\otimes_A A/I$.
+is the kernel of $B \to B \widehat{\otimes}_A A/I$.
 \end{lemma}
 
 \begin{proof}
@@ -865,7 +865,7 @@ \section{Topological rings and modules}
 Let $I_\mu$ be a fundamental system of open ideals in $A$.
 Then
 $$
-B \widehat\otimes_A A/I = \lim (B/J_\lambda \otimes_A A/(I_\mu + I)) =
+B \widehat{\otimes}_A A/I = \lim (B/J_\lambda \otimes_A A/(I_\mu + I)) =
 \lim B/(J_\lambda + I_\mu B + I B)
 $$
 Since $A \to B$ is continuous, for every $\lambda$ there
@@ -2248,7 +2248,7 @@ \section{Separation axioms for formal algebraic spaces}
 \item If $X$, $Y$, and $Z$ are McQuillan formal algebraic spaces
 corresponding to the weakly admissible topological $S$-algebras
 $A$, $B$, and $C$, then $X \times_Z Y$ corresponds to
-$A \widehat\otimes_C B$.
+$A \widehat{\otimes}_C B$.
 \end{enumerate}
 \end{lemma}
 
@@ -2795,7 +2795,7 @@ \section{Morphisms representable by algebraic spaces}
 }
 $$
 By Lemma \ref{lemma-fibre-product-affines-over-separated}
-we see that $B/J(I) = B \widehat\otimes_A A/I$.
+we see that $B/J(I) = B \widehat{\otimes}_A A/I$.
 It follows that $J(I)$ is the closure of the ideal $\varphi(I)B$, see
 Lemma \ref{lemma-closure-image-ideal}.
 Since $\text{Spf}(A) = \colim \Spec(A/I)$ with $I$ as above,