Workshop "The Mordell-Weil Theorem"

The “Mordell-Weil theorem” workshop is hosted by the Vietnam Institute of Mathematics aiming to master students from Vietnam and other countries who are interested in Algebraic Geometry. The objective of the workshop is to provide a forum for master students to foster links and collaboration among themselves.

This workshop provides the most fundamental concepts of the Arithmetic of The Elliptic Curves, following Silverman's text. Starting with basic notions from classical Algebraic Geometry: Varieties, Curves, Riemann-Roch Theorem... we work on several topics such as The Formal Group, Hasse Theorem and Weil Conjectures, connections with elliptic functions and the Lefschetz Principle. Then, our aim is to give a proof of the famous Mordell-Weil Theorem, which asserts that the group $E(K)$ of rational points of an Elliptic Curve $E$ defined over a number field $K$ is a finitely generated abelian group. An algorithm computing this group is still being sought. We will however illustrate the "Descent by Isogeny" method, which often works.