A morphism of finite type is a morphism 
of schemes such that, for
every affine scheme 
open in 
, the inverse image 
has a finite cover by affine schemes 
for which every 
is generated by finitely many elements as an 
-algebra.
The composition of morphisms of finite type is of finite type, and every base change of a morphism of finite type is of finite type. Every proper morphism is of finite type.
