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Definition 65.12.5. Let $S \in \mathop{\mathrm{Ob}}\nolimits (\mathit{Sch}_{fppf})$ be a scheme. Let $F$ be an algebraic space over $S$. A Zariski covering $\{ F_ i \subset F\} _{i \in I}$ of $F$ is given by a set $I$ and a collection of open subspaces $F_ i \subset F$ such that $\coprod F_ i \to F$ is a surjective map of sheaves.

Comments (2)

Comment #2040 by Keenan Kidwell on

The third sentence is awkward; maybe delete the comma and replace it with the word "and?"

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  • 4 comment(s) on Section 65.12: Immersions and Zariski coverings of algebraic spaces

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View Definition 65.12.5 as pdf