I was thinking to start reading the proof of Mordell-Weil Theorem for abelian varieties over number fields, after getting done with the proof in the case of elliptic curves over number field and I wasn't sure how to go on about it.

As of now, I am familiar with the basic Algebraic Geometry (classical, affine and projective varieties' theory included in the first introduction to the course, although I'll have to brush up on Riemann- Roch theorem quite a bit) and also the proof in case of Elliptic Curves over number fields using cohomological approach.

I've heard that the more generalized result in case of abelian varieties uses quite a bit of AG, so this post is to ask what kind of AG is needed to be able to read/understand the proof? Can someone recommend some references for it with possibly some reviews about them or maybe suggest a path that one should follow if they're interested in the proof?

Thank you in advance.

Diophantine Geometry, Mumford'sAbelian Varieites, ...), and a discussion of their respective merits would be good answers to this question, as would a discussion of the requisite background. $\endgroup$1more comment