This relates to this post.

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 theories 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 had studied Hartshorne.
But glancing through it, it seems to be so hard for such people.
Did he mean that I should read it with other papers (such as Katz or Deligne-Rapoport), or using some theories as a blackbox? (And in general, how should I read papers? I've never really read papers before...)

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!

  • 4
    $\begingroup$ You need to learn about modular forms for most of those papers but other than that I don't think there is a standard path from here on. Pick a big paper you like and figure out what knowledge you are missing. I especially like this lecture series www-personal.umich.edu/~asnowden/teaching/2013/679 $\endgroup$
    – Asvin
    Aug 31, 2019 at 14:46


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