I.3.20

This has H = 1

HAPPY
<math f\in A(Y-P)
 * Consider $$ V(f) \subset Y-p$$. If $$p$$ is in the clsoure (taken in $$Y$$), then extend by zero.
 * Otherwise $$p$$ is not in the closure, argue $$ 1/f \in A(U - p)$$ for a sufficiently small $$U \ni p$$ disjoint from $$V(f)$$
 * Argue in fact 1/f \in \mathcal{O}_p; for all $$ q \in U-p$$, $$ 1/f = g/h$$ near $$q$$
 * If $$h(p) = 0$$ use $$ \dim Y \ge 2$$ to show $$ V(f) \cap U \ne \emptyset$$; contradiction.
 * Consider $$J \subset \{g \in \mathcal{O}_p| fg \in \mathcal{O}_p\}$$
 * By the above, conclude f^nJ \subset J.
 * Show $$f$$ is integral over $$\mathcal{O}_p$$.