Alladi Ramakrishnan Hall

Why is Serre’s problem difficult ?

L. Merel

University of Paris VII

We will explain why (in our opinion) the difficulty to solve Serre’s problem stems
from the same reason than the difficulty of Diophantus’ equation of lecture 1. For
that, we will use Chen’s theorem and we will make a detour through modular
jacobians, modular forms and the Birch and Swinnerton-Dyer conjecture.

Prerequisite : Basic algebraic number theory. The talk can be understood as a little
survey of the arithmetic of modular forms.