In this thesis we give an exposition of John Tate's doctoral dissertation titled `Fourier
Analysis in Number Fields and Hecke's Zeta-Functions'. In this dissertation, Tate
proved the analytic continuation and functional ...
The goal of the project is to study Class Field Theory. Class Field Theory studies the
abelian extensions of local elds and global elds. There are di erent approaches for this
and we focus on the cohomological approach ...
The central objective of this thesis is to state and prove the main theorems of local and global
class field theory. We first give a brief overview of basic algebraic number theory followed by
group cohomology. Then, we ...