Definition 10.122.3. Let $R \to S$ be a finite type ring map. Let $\mathfrak q \subset S$ be a prime.
If the equivalent conditions of Lemma 10.122.2 are satisfied then we say $R \to S$ is quasi-finite at $\mathfrak q$.
We say a ring map $A \to B$ is quasi-finite if it is of finite type and quasi-finite at all primes of $B$.