0Introduction

IV Topics in Number Theory



0 Introduction
In this course, we shall first give an outline of class field theory. We then look at
abelian
L
-functions (Hecke, Tate). We then talk about non-abelian
L
-functions,
and in particular the Weil–Deligne group and local L- and ε-factors.
We then talk about local Langlands for
GL
n
a bit, and do a bit of global
theory and automorphic forms at the end.
The aim is not to prove everything, because that will take 3 courses instead of
one, but we are going to make precise definitions and statements of everything.