Generalized ambiguous logarithmic classes
type: Item
instance of: scholarly article
title: Generalized ambiguous logarithmic classes
zbMATH Open document ID: 0953.11035
DOI: 10.1007/BF02942570
author: Yanyan Li
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2000-03-19T00:00:00Z
review text: For a number field \(k\) and a fixed prime \(l\), the \(l\)-group of logarithmic classes \(\widetilde{Cl}_k\) has been defined by \textit{J.-F. Jaulent} in [J. Théor. Nombres Bordeux 6, 301-325 (1994; Zbl 0827.11064)]. In this note, given a cyclic \(l\)-extension \(K/k\), with \(G= \text{Gal} (K/k)\), the author considers quotients of \(\widetilde{Cl}_k\) by sub-\(G\)-modules \(\widetilde{\mathcal H}_k\) and proves a formula for the order of \((\widetilde{Cl}_k/ \widetilde{\mathcal H}_k)^G\) in the style of genus theory.
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11R23
zbMATH DE Number: 1416654
zbMATH Keywords: logarithmic classes
reviewed by: Thong Nguyen Quang Do
MaRDI profile type: Publication
cites work: Generalized invariant classes
cites work: On the 2-component of the class group of certain cyclic extensions of degree \(2^ n\)
cites work: Q4010511
cites work: Sur le noyau sauvage des corps de nombres
cites work: Classes logarithmiques ambiges des corps quadratiques
cites work: Sur les classes logarithmiques des CM -extensions
description: scientific article; zbMATH DE number 1416654