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

Luca Caputo — 2007

Journal de Théorie des Nombres 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 .

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