Logarithmic classes in the narrow sense
type: Item
instance of: scholarly article
title: Logarithmic classes in the narrow sense
zbMATH Open document ID: 0887.11044
DOI: 10.1007/BF02677481
author: M. García
published in: Manuscripta Mathematica
publication date: 1998-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/156309
review text: Let \(\ell\) be a prime. The concept of the logarithmic \(\ell\)-class group \(\widetilde{{\mathcal C}\ell}_K\) of a number field \(K\) has been introduced by \textit{J.-F. Jaulent} [J. Théor. Nombres Bordx. 6, 301-325 (1994; Zbl 0827.11064)]. It has its origin in studies of some \(\ell\)-extensions in connection with \(K\)-theory. A conjecture of Gross asserts that \(\widetilde{{\mathcal C}\ell}_K\) is finite. Take \(\ell=2\). The author introduces the concept of the logarithmic 2-class group in the narrow sense and investigates its properties. One of the main results is a formula for the ambiguous logarithmic classes in the case of a cyclic 2-extension \(L/K\) assuming that the finiteness conjecture is true.
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R70
zbMATH DE Number: 1054311
zbMATH Keywords: logarithmic class in the narrow sense
zbMATH Keywords: ambiguous class
reviewed by: Veikko Ennola
MaRDI profile type: Publication
cites work: Algorithmic approach to logarithmic class groups
cites work: Generalized invariant classes
cites work: Classes logarithmiques ambiges des corps quadratiques
description: scientific article; zbMATH DE number 1054311