The Stacks project

Definition 17.20.1. Let $f : X \to Y$ be a morphism of ringed spaces. Let $x \in X$. We say $f$ is flat at $x$ if the map of rings $\mathcal{O}_{Y, f(x)} \to \mathcal{O}_{X, x}$ is flat. We say $f$ is flat if $f$ is flat at every $x \in X$.

Comments (2)

Comment #4966 by Matthieu Romagny on

Typo : replace "We say f is said to be flat at x if..." by "We say f is flat at x if..."

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View Definition 17.20.1 as pdf