replace * by {-1}

Thanks to weng yi xiang
https://stacks.math.columbia.edu/tag/02US#comment-7843

modules.tex

@@ -660,26 +660,26 @@ \section{A canonical exact sequence}
 Denote $j : U \to X$ the open immersion and
 $i : Z \to X$ the closed immersion.
 For any sheaf of abelian groups $\mathcal{F}$ on $X$
-the adjunction mappings $j_{!}j^*\mathcal{F} \to \mathcal{F}$ and
-$\mathcal{F} \to i_*i^*\mathcal{F}$ give a short exact
+the adjunction mappings $j_{!}j^{-1}\mathcal{F} \to \mathcal{F}$ and
+$\mathcal{F} \to i_*i^{-1}\mathcal{F}$ give a short exact
 sequence
 $$
-0 \to j_{!}j^*\mathcal{F} \to \mathcal{F} \to i_*i^*\mathcal{F} \to 0
+0 \to j_{!}j^{-1}\mathcal{F} \to \mathcal{F} \to i_*i^{-1}\mathcal{F} \to 0
 $$
 of sheaves of abelian groups. For any morphism
 $\varphi : \mathcal{F} \to \mathcal{G}$ of abelian sheaves on $X$
 we obtain a morphism of short exact sequences
 $$
 \xymatrix{
 0 \ar[r] &
-j_{!}j^*\mathcal{F} \ar[r] \ar[d] &
+j_{!}j^{-1}\mathcal{F} \ar[r] \ar[d] &
 \mathcal{F} \ar[r] \ar[d] &
-i_*i^*\mathcal{F} \ar[r] \ar[d] &
+i_*i^{-1}\mathcal{F} \ar[r] \ar[d] &
 0 \\
 0 \ar[r] &
-j_{!}j^*\mathcal{G} \ar[r] &
+j_{!}j^{-1}\mathcal{G} \ar[r] &
 \mathcal{G} \ar[r] &
-i_*i^*\mathcal{G} \ar[r] &
+i_*i^{-1}\mathcal{G} \ar[r] &
 0
 }
 $$