Cohen-Lenstra heuristics and the Spiegelungssatz: function fields
type: Item
instance of: scholarly article
title: Cohen-Lenstra heuristics and the Spiegelungssatz: function fields
zbMATH Open document ID: 1049.11121
published in: Journal of Number Theory
publication date: 2004-08-04T00:00:00Z
review text: The author gives support to Cohen-Lenstra heuristics for cyclic function fields by showing its consistency with Leopoldt's Spiegelungssatz in this setting. The paper proceeds by reviewing basic function field theory so as to state a version of the Spiegelungssatz, then proves a group-theoretic version for cyclic function fields. Thereafter, the Friedman-Washington formulation of Cohen-Lenstra heuristics for certain function fields is generalized to the cyclic case. Checking compatibility, under an appropriate assumption, then gives the conclusion.
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R58
zbMATH DE Number: 2081157
zbMATH Keywords: Cohen-Lenstra heuristics
zbMATH Keywords: cyclic function field
zbMATH Keywords: class groups
zbMATH Keywords: Spiegelungssatz
author: Yoonjin Lee
reviewed by: Thomas A. Schmidt
MaRDI profile type: Publication
full work available at URL: j.jnt.2004.01.001
OpenAlex ID: W2029476171
cites work: Q3476914
cites work: Q3697109
cites work: Q3035404
cites work: Q4249697
cites work: Cohen-Lenstra heuristics and the Spiegelungssatz: number fields
cites work: Zur Struktur der l-Klassengruppe galoisscher Zahlkörper.
cites work: Q4135665
cites work: \(S\)-units and \(S\)-class group in algebraic function fields
cites work: The Hilbert class field in function fields
DOI: 10.1016/J.JNT.2004.01.001
description: scientific article; zbMATH DE number 2081157