Chapter 7 The main results
We finally embark on the proof of the main results of global class field theory, via the adelic reformulation (Section 6.4) and specifically the outline from Section 6.5.
As explained in the preface, the reader who has arrived at this point having skipped Chapter 5 still has the ability to obtain complete proofs of the main results. To do so, read Section 7.1 and Section 7.2 in their entirety (for the First Inequality and the Second Inequality); then skip ahead to Section 7.6 (for local-to-global compatibility, the reciprocity isomorphism, and the norm limitation theorem); then return to Section 7.4 (for the existence theorem).
