Principalization of ideals in abelian extensions of number fields

Sebastien Bosca, Georges Gras, Jean-François Jaulent

Published 2008-03-28, updated 2009-03-01Version 2

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 $k$