Théorie locale du corps de classes et $(\phi ,\Gamma )$-modules Lubin-Tate

Abstract

We show how to deduce the determination of the maximal abelian extension of $F$, with $[F:{\mathbf{Q}}_p]<\infty$, from the theory of Lubin-Tate $(\phi ,\Gamma )$-modules.

The proof of Lemma 14 is an hallucination, hence the main theorem is not proved