Definition 41.3.1. Let $A$, $B$ be Noetherian local rings. A local homomorphism $A \to B$ is said to be unramified homomorphism of local rings if
$\mathfrak m_ AB = \mathfrak m_ B$,
$\kappa (\mathfrak m_ B)$ is a finite separable extension of $\kappa (\mathfrak m_ A)$, and
$B$ is essentially of finite type over $A$ (this means that $B$ is the localization of a finite type $A$-algebra at a prime).