Definition 73.7.7. Let $S$ be a scheme. Let $(\textit{Spaces}/S)_{fppf}$ be as in Definition 73.7.6. Let $X$ be an algebraic space over $S$, i.e., an object of $(\textit{Spaces}/S)_{fppf}$. Then the big fppf site *$(\textit{Spaces}/X)_{fppf}$* of $X$ is the localization of the site $(\textit{Spaces}/S)_{fppf}$ at $X$ introduced in Sites, Section 7.25.

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