Principalization of ideals in abelian extensions of number fields

Abstract

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 $K{k}^{ab}$ of $K$ with the maximal abelian extension $k^{ab}$ of $k$

Cited by in corpus (4)

• Invariant generalized ideal classes -- structure theorems for p-class groups in p-extensions
• Practice of incomplete p-ramification over a number field -- History of abelian p-ramification
• The Chevalley-Herbrand formula and the real abelian Main Conjecture
• Principalization of logarithmic class groups