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

Stéphanie Reglade

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

Number Theory 2013-03-29 v3

Authors: Stéphanie Reglade

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.

Keywords

class field theory ell-adic Neukirch framework degree maps G-modules valuations class field axiom

Cite

@article{arxiv.1211.1476,
  title  = {A formal approach "\`a la Neukirch" of $\ell$-adic class field theory},
  author = {Stéphanie Reglade},
  journal= {arXiv preprint arXiv:1211.1476},
  year   = {2013}
}

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