 Morphism of finite type

A morphism $f:X\to Y$ is of finite type when every point of $Y$ has an affine neighborhood $V=\mathrm{Spec}A$ for which $f^{-1}V$ has a finite affine cover $\mathrm{Spec}{B}_i$ with each $B_i$ a finitely generated $A$-algebra.

In algebraic geometry, the notion of a morphism of finite type is a crucial concept used to describe the relationship between schemes or algebraic varieties. It gives a way to define morphisms that are "nice" in a certain sense, particularly in terms of the structure of the spaces involved.