Definition 15.82.1. Let $A \to B$ be a ring map.

1. We say $A \to B$ is a pseudo-coherent ring map if it is of finite type and $B$, as a $B$-module, is pseudo-coherent relative to $A$.

2. We say $A \to B$ is a perfect ring map if it is a pseudo-coherent ring map such that $B$ as an $A$-module has finite tor dimension.

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