I've got most of a proof of Chow's Lemma worked out following the sketch in Hartshorne. I wanted to compare notes with what was on the internet and was pleased to see wikipedia had a proof of this fact.
Unfortunately, at the end, the proof gets pretty bizarre. There are a handful of maps that don't appear to be defined anywhere else, and the last argument appears to be a diagram chase with no diagram. I've tried to reconstruct this diagram myself just from seeing the apparent commutativtity relations, but I appear to have twisted myself up in knots.
Can anyone help me straighten out the end of the proof here? Here's a link to the page.