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December 2019 Principalisation abélienne des groupes de classes logarithmiques
Jean-François Jaulent
Funct. Approx. Comment. Math. 61(2): 257-275 (December 2019). DOI: 10.7169/facm/1765

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 $\ell$ and where at least one of the infinite places completely splits, we prove that there exists infinitely many abelian $\ell$-extensions $F/k$ such that the relative subgroup $\mathcal{C}\ell_{K/k} = \Ker (\mathcal{C}\ell_K\to\mathcal{C}\ell_\k)$ of the $\ell$-group of logarithmic classes of $K$ capitulates in the compositum $FK$.

Citation

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Jean-François Jaulent. "Principalisation abélienne des groupes de classes logarithmiques." Funct. Approx. Comment. Math. 61 (2) 257 - 275, December 2019. https://doi.org/10.7169/facm/1765

Information

Published: December 2019
First available in Project Euclid: 26 October 2019

zbMATH: 07149360
MathSciNet: MR4042394
Digital Object Identifier: 10.7169/facm/1765

Subjects:
Primary: 11R37
Secondary: 11R20

Keywords: logarithmic classes , principalization

Rights: Copyright © 2019 Adam Mickiewicz University

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Vol.61 • No. 2 • December 2019
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