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I would love to know some good refercences about Elliptic curves over function fields. Especially in view with Mordell-Weil's Theorem. I am already familiar with the main proof of Mordell's theorem in the book "Rational Points on Elliptic Curves" by Silverman-Tate, thus I am already familiar with the case over $\mathbb{Q}$.

Does anyone have any suggestions?

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  • $\begingroup$ Silverman has another book, at the graduate level, called Arithmetic of Elliptic Curves. $\endgroup$ – Future Feb 1 '16 at 17:40
  • $\begingroup$ I am also already familiar with that book, but it sadly does not discuss the case over function fields $\endgroup$ – Mathemagician Feb 1 '16 at 17:47
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There are fairly detailed notes by Douglas Ulmer available online. They cover the important case of function fields over finite fields. I couldn't tell if this is the case that interest you.

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There is Elliptic Curves: Number Theory and Criptography by Lawrence, where on chapter 8 the author treats this subject.

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  • $\begingroup$ Thank you, I also have another book with the same name by Washington. Is it the same book you are referring to? $\endgroup$ – Mathemagician Feb 1 '16 at 18:14
  • $\begingroup$ I've studied with this book. Yes, it's Lawrence C. washington $\endgroup$ – Aaron Maroja Feb 1 '16 at 18:15
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See the book "Lectures on the Mordell-Weil Theorem" of Jean-Pierre Serre.

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    $\begingroup$ Why is this a good choice? $\endgroup$ – Rory Daulton Feb 7 '16 at 1:04

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