How to define a profinite morphism What is the definition of a profinite morphism in http://www.math.upenn.edu/~pop/Teaching/2010_Math624/2010_Math624PS08.pdf problem 5? This is not actually a homework of mine but I was unable to find the definition.
Snapshot:


A profinite morphism presumably means something like a projective limit of finite morphisms.  Since finite morphisms are affine, we can think what this would mean in terms of maps of affine schemes.  An inductive limit of finite maps
$R \to S_i$ is the same as a map $R \to S$ where $S$ is integral over $R$,
so this leads me to guess that a profinite morphism is a morphism $X \to Y$
which is affine, and so that on affine opens Spec $R$ in $Y$, the preimage
in $X$ is of the form Spec $S$ with $S$ integral over $R$.  
This is compatible with exercise 1 (b), and exercise 5, on the assignment that you link to.  Note, though, that as others have already pointed out, assuming that my guess is correct, this terminology is not standard, or at least not common.  More typically, such morphisms 
are called integral.  (This is the terminology used in Ravi Vakil's notes, and presumably also in the stacks project, and I also presume it is the terminology used in EGA.)
