In this course we will study the main results of global class field theory via applications to more advanced topics in number theory. The emphasis will be on applications and not on the proofs of class field theory.
Topics to be discussed, depending on time, include Selmer groups, rational points on elliptic curves, Tate's theorem on projective Galois representations, Hecke theory for characters, Deligne's local epsilon factors for Galois representations, Iwasawa theory for cyclotomic extensions.
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