Ben Rosenfield Class Field Theory

This is the second iteration of my notes on class field theory. I am attempting to prove (what I feel are) the the essential facts of class field theory in a way that I find attractive (bounded above by my lack of experience, time constraints, and ennui). This note is still not quite complete and can be imprecise in places. This will be straightened out as time goes on. A list of spots that need work (and will be worked on in the near future): Section 1.4, (25), (29), Section 2.5, (38), (42), Global Kummer Case, Section 3.7; I may also make the homological algebra section more self-contained. These results are basically true for function fields, with minor alterations, but I am only doing this for number fields. Corrections/suggestions, etc are always welcome (rosenfie(at)math.umn.edu). Finally, I should mention that I have not been uniform in my notation. This will be fixed in the next iteration. Caveat Emptor.