A classification of the extensions of degree p^2 over Q_p whose normal closure is a p-extension

Luca Caputo (1)

1 IMB - Institut de Mathématiques de Bordeaux

Let k be a finite extension of Q_p and E_k be the set of the extensions of degree p^2 over k whose normal closure is a p-extension. For a fixed discriminant, we show how many extensions there are in E_{Q_p} with such discriminant and we give the discriminant and the Galois group (together with its filtration of the ramification groups) of their normal closure. We show how this method can be generalized to get a classification of the extensions in E_k.

Mots clés: p-adic extensions; ramification groups; discriminant

Domaines: Théorie des nombres [math.NT]

Luca Caputo. A classification of the extensions of degree p^2 over Q_p whose normal closure is a p-extension. Journal de Théorie des Nombres de Bordeaux, 2007, pp.337. ⟨hal-00268079⟩