Locally of finite type
= Locally of finite type
A <morphism of schemes> $f:X\to S$ is locally of finite type if, over every <affine open subscheme> $\operatorname{Spec}A\subseteq S$, its inverse image is covered by <affine schemes> $\operatorname{Spec}B$ with $B$ a finitely generated $A$-<algebra>. It is of <finite type> exactly when it is also a <quasi-compact morphism>.