This relates to [this post](https://mathoverflow.net/questions/21552/roadmap-for-studying-arithmetic-geometry?rq=1).

I want to study arithmetic, such as Fermat's last theorem, Faltings' theorem, Mazur's torsion points theorem, Weil conjecture and so on.   
For understanding these theorems (or other important arithmetic theorems), what should I study?
I want to know some papers or texts.

In the post, Emerton said that Mazur's paper "Modular curves..." is really good for those who study Hartshorne.   
But glancing through it, I feel that this is far from my background.   
Did he means that I should read it with other papers (such as Katz or Deligne-Rapoport), or using some theories as a blackbox?

My background is some elementary algebraic geometry and algebraic number theory, e.g., Hatshorne's AG, Liu's "AG and...", Neukirch's "Algebraic Number theory", Serre's "Local Fields" and Silverman's AEC.
And I have studied a little abelian variety and elale cohomology.

Any help will be much appreciated!