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Dimension and qf maps in decent-spaces

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aisejohan committed Dec 6, 2017
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@@ -2317,6 +2317,17 @@ \section{Points on spaces}
This is Algebra, Lemma \ref{algebra-lemma-dimension-inequality-quasi-finite}.
\end{proof}
\begin{lemma}
\label{lemma-dimension-quasi-finite}
Let $S$ be a scheme. Let $X \to Y$ be a locally quasi-finite morphism
of algebraic spaces over $S$. Then $\dim(X) \leq \dim(Y)$.
\end{lemma}
\begin{proof}
This follows from Lemma \ref{lemma-dimension-local-ring-quasi-finite}
and Properties of Spaces, Lemma \ref{spaces-properties-lemma-dimension}.
\end{proof}
\noindent
The following lemma is a tiny bit stronger than
Properties of Spaces,

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