The Stacks project

Definition 87.34.1. Let $S$ be a scheme. Let $X$ be a formal algebraic space with reduction $X_{red}$ (Lemma 87.12.1).

  1. The small étale site $X_{\acute{e}tale}$ of $X$ is the site $X_{red, {\acute{e}tale}}$ of Properties of Spaces, Definition 66.18.1.

  2. The site $X_{spaces, {\acute{e}tale}}$ is the site $X_{red, spaces, {\acute{e}tale}}$ of Properties of Spaces, Definition 66.18.2.

  3. The site $X_{affine, {\acute{e}tale}}$ is the site $X_{red, affine, {\acute{e}tale}}$ of Properties of Spaces, Lemma 66.18.6.

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