Principalisation abélienne des groupes de classes logarithmiques

Abstract

We extend to logarithmic class groups the results on abelian principalization of tame ray class groups of a number field obtained in a previous article. As a consequence, for any extension K/k of number fields which satisfies the Gross-Kuz'min conjecture for the prime l and where at least one of the infinite places completely splits, we prove that there exists infinitely many abelian l-extensions F/k such that the relative subgroup of the l-group of logarithmic classes of K capitulates in the compositum FK.