II.4.6

This has H = 2, V = ...; ex. II.4.1 can be applied.

HAPPY
Say $$\mbox{Spec }B = X \xrightarrow{f} Y =\mbox{Spec }A$$ is determined by $$ \theta \colon A \to B$$.
 * Replace $$ A$$ with $$A/\ker \theta$$ and use II.4.1 to reduce to the case $$ \theta $$ injective.
 * Show there are injections $$ A \subset B \subset \overline{A}$$ where the last is the integral closure (in the fraction field of B).
 * use 4.11A to reduce this to $$ B \subset R_v$$ for all valuation rings (of $$K(B)/k$$) containing $$A$$
 * use the valuation ring criterion of properness.