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smooth morphism of schemes

A morphism $f : X \to Y$ of schemes is smooth if it is flat and finitely presented (cf. relativization in algebraic geometry) and if all the fibers $f^{- 1} (y)$ where $y \in Y$ are smooth schemes over the corresponding residue fields $k_{y}$ .

Smoothness of a morphism is a weaker notion than the notion of a morphism being étale, but stronger than the notion of formal smoothness.