# The Stacks Project

## Tag 01BO

Lemma 17.11.2. Let $(X, \mathcal{O}_X)$ be a ringed space. Any $\mathcal{O}_X$-module of finite presentation is quasi-coherent.

Proof. Immediate from definitions. $\square$

The code snippet corresponding to this tag is a part of the file modules.tex and is located in lines 1424–1429 (see updates for more information).

\begin{lemma}
\label{lemma-finite-presentation-quasi-coherent}
Let $(X, \mathcal{O}_X)$ be a ringed space.
Any $\mathcal{O}_X$-module of finite presentation
is quasi-coherent.
\end{lemma}

\begin{proof}
Immediate from definitions.
\end{proof}

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