Let's say a morphism $f:X\to Y$ is compactifiable if it admits a factorization $f = pj$ with $j:X\to P$ an open immersion and $p:P\to Y$ proper.
In SGA 4 Exp. XVII, Deligne says that Nagata proved that any morphism of separated integral northerian schemes is compactifiable but that he didn't understand the proof.
- Where can I find a proof of Nagata's theorem?
- What about the complex analytic setting?