Locally of finite presentation

A morphism $f:Y\to X$ of schemes is locally of finite presentation if $X$ has an affine open cover $U_i=\operatorname{Spec}A_i$ such that each $f^{-1}(U_i)$ has an affine open cover $V_{ij}=\operatorname{Spec}B_{ij}$ for which every $A_i$-algebra $B_{ij}$ is finitely presented.

Explicitly, finitely presented means that for some finite integers $m,n$,

This criterion is local on both source and target; the resulting property is independent of the chosen affine covers.

For a field extension $K/F$, $\operatorname{Spec}K\to\operatorname{Spec}F$ is locally of finite presentation exactly when $K$ is a finitely presented $F$-algebra. In particular, every finite field extension has this property.