| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 101 === Let K be a number eld and E=K be an elliptic curve, that is, a smooth projective
curve of genus 1 with an distinguished K-rational point chosen. By the Mordell-Weil
Theorem, the group of points E(K) is a nitely generated abelian group. Its structure
is of the form:
E(K) = Etors(K) Zr
According to this theorem, we know that Etors(K) is a nite group. In 1977, Mazur
[Maz] proved a beautiful theorem for K = Q. It determines all the possible torsion
structures of Etors(Q).
In this thesis, we try to survey on the proof of this tremendous theorem as well as that
of Mordell-Weil Theorem.
|
|---|
