The Stacks project

Definition 67.38.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$.

  1. We say $f$ is unramified if the equivalent conditions of Lemma 67.22.1 hold with $\mathcal{P} = \text{unramified}$.

  2. Let $x \in |X|$. We say $f$ is unramified at $x$ if there exists an open neighbourhood $X' \subset X$ of $x$ such that $f|_{X'} : X' \to Y$ is unramified.

  3. We say $f$ is G-unramified if the equivalent conditions of Lemma 67.22.1 hold with $\mathcal{P} = \text{G-unramified}$.

  4. Let $x \in |X|$. We say $f$ is G-unramified at $x$ if there exists an open neighbourhood $X' \subset X$ of $x$ such that $f|_{X'} : X' \to Y$ is G-unramified.

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View Definition 67.38.1 as pdf