User:Freetiger18/Morphism of finite type

A morphism of finite type.

A morphism $f: X \rightarrow Y$ is locally of finite type if $Y$ can be covered by open sets $V_i = \mathrm{Spec} B_i$, such that for each $i$, $V_i$ can be covered by open affine subsets $U_ij = \mathrm{Spec} A_ij$, with each $A_ij$ a finitely-generated $B_i$ algebra. It is of finite type, if in addition for each $i$ the number of $U_ij$ required is finite.