Lemma 34.9.11. Let $T$ be a scheme. Let $\{ f_ i : T_ i \to T\} _{i \in I}$ be a family of morphisms of schemes with target $T$. Assume that

each $f_ i$ is flat, and

every affine scheme $Z$ and morphism $h : Z \to T$ there exists a standard fpqc covering $\{ Z_ j \to Z\} _{j = 1, \ldots , n}$ which refines the family $\{ T_ i \times _ T Z \to Z\} _{i \in I}$.

Then $\{ f_ i : T_ i \to T\} _{i \in I}$ is an fpqc covering of $T$.

## Comments (2)

Comment #3203 by Dario Weißmann on

Comment #3307 by Johan on

There are also: