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Definition 34.5.1. Let $T$ be a scheme. A smooth covering of $T$ is a family of morphisms $\{ f_ i : T_ i \to T\} _{i \in I}$ of schemes such that each $f_ i$ is smooth and such that $T = \bigcup f_ i(T_ i)$.

Comments (5)

Comment #3517 by Samir Canning on

small typo: "an smooth" should be "a smooth."

Comment #3518 by Raymond Cheng on

Heh. This goes all the way through the other topologies too. This is what happens when you copy and paste, starting with "étale"...

Comment #4724 by Théo de Oliveira Santos on

Has the "an smooth" vs "a smooth" correction been reversed?

There are also:

  • 3 comment(s) on Section 34.5: The smooth topology

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View Definition 34.5.1 as pdf