Lecture Notes: An invitation to modular forms
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چکیده
1 Tate's thesis in the context of class field theory 1.1 Reciprocity laws Let K be a number field or function field. Let C K = A × K /K × be the idele class group. One of the main theorems of class field theory is the existence of a reciprocity map rec K : C K → Gal(K ab /K). This map is continuous with dense image. Whenever L/K is a finite abelian extension, there is a relative version of the above map, call it rec L/K , that makes the diagram commute:
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