On class groups of random number fields

Bartel, A. and Lenstra Jr., H. W. (2020) On class groups of random number fields. Proceedings of the London Mathematical Society, 121(4), pp. 927-953. (doi: 10.1112/plms.12343)

177305.pdf - Published Version
Available under License Creative Commons Attribution.



The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the probability weights appearing in the general form of the heuristics. We conclude by proposing a rigorously formulated Cohen--Lenstra--Martinet conjecture.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bartel, Professor Alex
Authors: Bartel, A., and Lenstra Jr., H. W.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Proceedings of the London Mathematical Society
Publisher:London Mathematical Society
ISSN (Online):1460-244X
Published Online:18 May 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Proceedings of the London Mathematical Society 121(4):927-953
Publisher Policy:Reproduced under a Creative Commons license
Related URLs:

University Staff: Request a correction | Enlighten Editors: Update this record

Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
174023Cohen-Lenstra heuristics, Brauer relations, and low-dimensional manifoldsAlex BartelEngineering and Physical Sciences Research Council (EPSRC)EP/P019188/1M&S - Mathematics