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

Stéphanie Reglade (1)

1 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Class field theory

Domaines: Théorie des nombres [math.NT]

Stéphanie Reglade. A formal approach "à la Neukirch" of $\ell$-adic class field theory. 2013. ⟨hal-00749232v3⟩