Principalization of ideals in abelian extensions of number fields

Sebastien Bosca (1) , Georges Gras (2) , Jean-François Jaulent (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 Chercheur indépendant

We give the complete proof of a conjecture of Georges Gras which claims that, for any extension $K/k$ of number fields in which at least one infinite place is totally split, every ideal $I$ of $K$ principalizes in the compositum $Kk^{ab}$ of $K$ with the maximal abelian extension $k^{ab}$ of $k$

Mots clés: principalization; capitulation; Gras conjecture

Domaines: Théorie des nombres [math.NT]

Sebastien Bosca, Georges Gras, Jean-François Jaulent. Principalization of ideals in abelian extensions of number fields. International Journal of Number Theory, 2009, 5, pp.1--13. ⟨hal-00267830v2⟩