Séance Séminaire

Séminaire de Théorie des Nombres de Montpellier

Explicit local class field theory meets non-abelian extensions

We will explain how one can compute Galois groups of some non-abelian extensions of local fields entirely using class field theory. For this purpose we will explain some ideas of recent (non-Langlands-type) non-abelian generalizations of local class field theory. We will focus on demonstrating that some of these methods can be brought into a very explicit shape.