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

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