Definition 72.9.1. Let $S$ be a scheme, and let $X$ be an algebraic space over $S$. An *fpqc covering of $X$* is a family of morphisms $\{ f_ i : X_ i \to X\} _{i \in I}$ of algebraic spaces such that each $f_ i$ is flat and such that for every affine scheme $Z$ and morphism $h : Z \to X$ there exists a standard fpqc covering $\{ g_ j : Z_ j \to Z\} _{j = 1, \ldots , m}$ which refines the family $\{ X_ i \times _ X Z \to Z\} _{i \in I}$.

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