Definition 17.20.3. Let f : (X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y) be a morphism of ringed spaces. Let \mathcal{F} be a sheaf of \mathcal{O}_ X-modules.
We say that \mathcal{F} is flat over Y at a point x \in X if the stalk \mathcal{F}_ x is a flat \mathcal{O}_{Y, f(x)}-module.
We say that \mathcal{F} is flat over Y if \mathcal{F} is flat over Y at every point x of X.
Comments (0)