# stacks/stacks-project

typos in local-cohomology

 @@ -1439,8 +1439,8 @@ \section{Finiteness of pushforwards, I} Note that $\text{Ass}(\mathcal{F}') \subset \text{Ass}(\mathcal{F})$, see Divisors, Lemma \ref{divisors-lemma-ses-ass}. Since $\text{length}_{\mathcal{O}_{X, x}}(\mathcal{F}') = \text{length}_{\mathcal{O}_{X, x}}(\mathcal{F}) - 1$ $\text{length}_{\mathcal{O}_{X, x}}(\mathcal{F}'_x) = \text{length}_{\mathcal{O}_{X, x}}(\mathcal{F}_x) - 1$ we may apply the induction hypothesis to conclude $j_*\mathcal{F}'$ is coherent. Since $\mathcal{G} = j_*(\mathcal{G}|_U) = j_*i_{x, *}\mathcal{O}_{W_x}$ @@ -1468,7 +1468,7 @@ \section{Finiteness of pushforwards, I} $\varphi : \mathcal{G}|_U \to \mathcal{F}$. Then $\varphi$ is injective (for example by Divisors, Lemma \ref{divisors-lemma-check-injective-on-ass}) and we find and injective map and we find an injective map $\mathcal{G} = j_*(\mathcal{G}|_V) \to j_*\mathcal{F}$. Thus (1) holds. \end{proof} @@ -1661,7 +1661,7 @@ \section{Finiteness of pushforwards, I}  We have $j_*i_{x, *}\mathcal{O}_{W_x} = i_*j'_*\mathcal{O}_{W_x}$. As the left vertical arrow is a closed immersion we see that $j_*i_{x, *}\mathcal{O}_{W_x}$ is coherent if and only of $j_*i_{x, *}\mathcal{O}_{W_x}$ is coherent if and only if $j'_*\mathcal{O}_{W_x}$ is coherent. \end{remark}