Lemma 67.34.1. Let S be a scheme. Let f : X \to Y be a morphism of algebraic spaces over S. Let x \in |X|. Assume f is locally of finite type. Then we have
\begin{matrix} \text{relative dimension of }f\text{ at }x
\\ =
\\ \text{dimension of local ring of the fibre of }f\text{ at }x
\\ +
\\ \text{transcendence degree of }x/f(x)
\end{matrix}
where the notation is as in Definition 67.33.1.
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