Definition 37.21.1. Let f : X \to Y be a morphism of schemes. Assume that all the fibres X_ y are locally Noetherian schemes.
Let x \in X, and y = f(x). We say that f is regular at x if f is flat at x, and the scheme X_ y is geometrically regular at x over \kappa (y) (see Varieties, Definition 33.12.1).
We say f is a regular morphism if f is regular at every point of X.
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