if a map Y->X of schemes is finite then it is like a branched cover over X with finite fibers.

if it is just integral, should i think of that as being something like a branched cover with *pro*-finite fibers???

seems right idk

cuz like

if B is an integral A-algebra then it is the colimit of finite subalgebras. then dualize etc.

does this globalize properly? is it even the right intuition?? is there a way to make it into a precise statement???

idk man

@SC_Griffith