Exp 47: Nonabelian generalisation of local CFT
Exp 83: Weil on class field theory
Class field theory folder
Cox: Primes of the form etc, is an excellent book
http://londonnumbertheory.wordpress.com/2009/10/07/questions-on-class-field-theory/ mentions among other things an analogy between generalized Jacobians and what I think is ray class groups wrt some modulus.
http://londonnumbertheory.wordpress.com/2009/10/15/computational-class-field-theory/
Ulrich Thiel: Mackey functors and abelian class field theories. Abstract: Motivated by the work of Jürgen Neukirch and Ivan Fesenko we propose a general definition of an abelian class field theory from a purely group-theoretical and functorial point of view. This definition allows a modeling of abelian extensions of a field inside more general objects than the invariants of a discrete module over the absolute Galois group of the field. The main objects serving as such models are cohomological Mackey functors as they have enough structure to make several reduction theorems of classical approaches work in this generalized setting and, as observed by Fesenko, they even have enough structure to make Neukirch’s approach to class field theories via Frobenius lifts work. This approach is discussed in full detail and in its most general setting, including the pro-P setting proposed by Neukirch. As an application and justification of this generalization we describe Fesenko’s approach to class field theory of higher local fields of positive characteristic, where the modeling of abelian extensions takes place inside the cohomological Mackey functor formed by the Milnor-Paršin K-groups. The motivation for this work (which is the author’s Diplom thesis) was the attempt to understand what a class field theory is and to give a single-line definition which captures certain common aspects of several instances of class field theories. We do not claim to prove any new theorem here, but we think that our general and uniform approach offers a point of view not discussed in this form in the existing literature.
nLab page on Class field theory