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Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

12 votes

Using algebraic geometry to understand class field theory

A good reference is Neukirch's Algebraic Number Theory. It takes the analogy between algebraic number theory and algebraic geometry seriously, and it includes coverage of class field theory. But you'd …
Michael Joyce's user avatar