Definition 34.10.7. Let $T$ be a scheme. A *V covering of $T$* is a family of morphisms $\{ T_ i \to T\} _{i \in I}$ of schemes such that for every affine open $U \subset T$ there exists a standard V covering $\{ U_ j \to U\} _{j = 1, \ldots , m}$ refining the family $\{ T_ i \times _ T U \to U\} _{i \in I}$.

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