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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
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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 …