Definition 15.40.1. A ring map $R \to \Lambda$ is regular if it is flat and for every prime $\mathfrak p \subset R$ the fibre ring

$\Lambda \otimes _ R \kappa (\mathfrak p) = \Lambda _\mathfrak p/\mathfrak p\Lambda _\mathfrak p$

is Noetherian and geometrically regular over $\kappa (\mathfrak p)$.

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