Approche formelle à la manière de Neukirch de la Théorie $\ell$-adique du corps des classes

Stéphanie Reglade (1)

1 IMB - Institut de Mathématiques de Bordeaux

On the one hand Neurkirch has developped general class field theory in his book "Class Field Theory", and on the other hand Jaulent has developped $\ell$-adic class field theory in his article "Théorie $\ell$-adique du corps des classes". The question is to know whether it is possible to deduce $\ell$-adic class field theory from abstract class field theory, which implies in both cases (local case and global case) to define the degree map, the $G$-module, the vauation and to prove class field axiom.

Mots clés: Class field theory

Domaines: Théorie des nombres [math.NT]

Stéphanie Reglade. Approche formelle à la manière de Neukirch de la Théorie $\ell$-adique du corps des classes. 2012. ⟨hal-00749232v1⟩