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Fall Tutorial 2017

Arithmetic of Elliptic Curves

This tutorial is an introduction to the arithmetic of elliptic curves. After introducing several equivalent definitions of elliptic curves, we will prove the Mordell-Weil theorem, which states that for an elliptic curve defined over a number field, the set of rational points forms a finitely generated Abelian group. Then we will go into the theory of complex multiplication, and hopefully will have time to discuss more advanced topics including Selmer groups, Tate curves, etc. The first half of the material overlaps heavily with the tutorial in the previous year.
Prerequisites: Students should be familiar with basic algebraic number theory. Having taking the undergraduate algebraic geometry class would be helpful, but not required. Though it might be a good idea to take this and algebraic geometry as the same time.
Contact: Zijian Yao,