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Does anyone know a reference for the proof of the finite generation of the Mordell-Weil group over finitely generated fields?

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up vote 3 down vote accepted

It is in Lang's book "Fundamentals of diophantine geometry", chapter 6: google book preview

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Neron did the finitely generated ground field (his thesis), and Lang-Neron together did a generalization. I needed to use Lang-Neron (really just Neron's part) in a paper, but personally found the Lang book unsuitable as a reference because everything hinges in the theory of the Chow trace whose development Lang gives only in the Weil Foundations style which is really hard to understand (in contrast with the modern spirit of the rest of that book). So I wrote an expository article on "modern" approach to Chow trace and deduction of Lang-Neron from it. It's on my webpage. – BCnrd Apr 10 '10 at 17:07
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By the way, Brian, perhaps you should promote your comment to an answer, with a link. I would certainly rather read your paper than Lang's book, for exactly the reasons you say. – Pete L. Clark Apr 10 '10 at 17:16
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Pete, I've decided to stop posting "answers" on MO, only making comments. It keeps things short & sweet, and I don't care about the "point" stuff. – BCnrd Apr 10 '10 at 18:08
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Dear Brian, Leaving aside "points", there are some technical reasons to prefer that sufficiently significant comments should appear as answers: essentially, we want to use the system in such a way so that a later reader gets pointed quickly to the most useful responses. As a fellow longwinded answerer, I appreciate that the length restriction for comments can be useful. Probably what will happen is that people will convert some of your comments to answers, with attribution to you. I suppose you'll be okay with that? – Pete L. Clark Apr 11 '10 at 4:54
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If you don't care for points, you could for example make all of your (future) answers community wiki. – Kevin H. Lin Apr 12 '10 at 8:08

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