A formal approach "\`a la Neukirch" of $\ell$-adic class field theory

Abstract

Neukirch developed abstract class field theory in his famous book "Class Field Theory". We show that it is possible to derive Jaulent's '-adic class field from Neukirch's framework. The proof requires in both cases (local case and global case) to define suitable degree maps, G-modules, valuations and to prove the class field axiom.