To be more specific, how much is needed to understand the book 'Rational points on elliptic curves' by Silverman?


migrated from mathoverflow.net Jul 29 '13 at 19:52

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  • $\begingroup$ A good handle at least on rings and modules is probably required. You will definitely need rings for the algebraic geometry side of it. $\endgroup$ – rfauffar Jul 29 '13 at 19:10
  • $\begingroup$ Thanks. Would you recommend having experience with complex analysis? $\endgroup$ – Jonas Jul 29 '13 at 19:12
  • $\begingroup$ Complex analysis is definitely good, but I'm not sure it would be a requirement. $\endgroup$ – rfauffar Jul 29 '13 at 20:15

This book has six chapters, and one needs perhaps different prerequisites for each chapter. For chapter $I$ and $II$, on geometry of cubic curves and points of finite order, just basic algebra is enough, together with plane curves (affine and projective). For elliptic curves over the complex numbers, a bit of complex analysis is required. For chapter $III$ and $IV$ on the group of rational points and cubic curves over finite fields, more algebra is needed (for example, for the proof of Mordell's theorem). For chapters $V$ and $VI$ on Integer points on cubic curves, and Complex multiplication, Galois representations, algebraic number theory, and algebraic geometry would be helpful.


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