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I want to study Mazur's torsion theorem for elliptic curves over $Q$ and its generalizations for number fields, i.e., papers by Kamienny, Kenku & Momose, Filip Najman. So please suggest to me what background I should have before starting to read the relevant papers. If you could offer me some books/papers/articles, I would be glad.

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Andrew Snowden has just finished teaching a course on Mazur's torsion theorem--video-taped lectures and extensive notes may be found here. I've watched several of the lectures; they are excellent.

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The general case over arbitrary number fields has been treated by Loïc Merel. A good place to start would be Bas Edixhoven's Bourbaki exposé Rational torsion points on elliptic curves over number fields, Séminaire Bourbaki, 36 (1993-1994), Exposé No. 782.

There is also an excellent set of notes by Joseph Œsterlé which were to be found on the ICTP website.

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  • $\begingroup$ I can't find the notes by Joseph Œsterlé on the ICTP website. Will you please cite the relevant link ? $\endgroup$
    – Andrew
    Commented Dec 13, 2013 at 7:07
  • $\begingroup$ @Andrew indico.ictp.it/event/a02005/contribution/1/material/0/0.pdf $\endgroup$
    – duje
    Commented Mar 26, 2016 at 11:46
  • $\begingroup$ @duje's link is in french. $\endgroup$
    – Shreya
    Commented Nov 12, 2019 at 9:08

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