Arakelov class groups of random number fields
| dc.contributor.author | Bartel, A | |
| dc.contributor.author | Johnston, H | |
| dc.contributor.author | Lenstra, HW | |
| dc.date.accessioned | 2024-05-03T10:01:17Z | |
| dc.date.issued | 2024-04-16 | |
| dc.date.updated | 2024-04-29T10:47:03Z | |
| dc.description.abstract | The main purpose of the paper is to formulate a probabilistic model for Arakelov class groups in families of number fields, offering a correction to the Cohen–Lenstra–Martinet heuristic on ideal class groups. To that end, we show that Chinburg’s Ω(3) conjecture implies tight restrictions on the Galois module structure of oriented Arakelov class groups. As a consequence, we construct a new infinite series of counterexamples to the Cohen–Lenstra–Martinet heuristic, which have the novel feature that their Galois groups are non-abelian. | en_GB |
| dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
| dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
| dc.format.extent | 1-24 | |
| dc.identifier.citation | Published online 16 April 2024 | en_GB |
| dc.identifier.doi | https://doi.org/10.1007/s00208-024-02862-4 | |
| dc.identifier.grantnumber | EP/P019188/1 | en_GB |
| dc.identifier.grantnumber | EP/N005716/1 | en_GB |
| dc.identifier.uri | http://hdl.handle.net/10871/135846 | |
| dc.identifier | ORCID: 0000-0001-5764-0840 (Johnston, Henri) | |
| dc.language.iso | en | en_GB |
| dc.publisher | Springer | en_GB |
| dc.rights | © The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | en_GB |
| dc.title | Arakelov class groups of random number fields | en_GB |
| dc.type | Article | en_GB |
| dc.date.available | 2024-05-03T10:01:17Z | |
| dc.identifier.issn | 0025-5831 | |
| dc.description | This is the final version. Available from Springer via the DOI in this record. | en_GB |
| dc.description | Data availability statement: Data sharing is not applicable to this article, as no datasets were generated or analysed during the present work. | en_GB |
| dc.identifier.eissn | 1432-1807 | |
| dc.identifier.journal | Mathematische Annalen | en_GB |
| dc.relation.ispartof | Mathematische Annalen | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
| dcterms.dateAccepted | 2024-03-25 | |
| rioxxterms.version | VoR | en_GB |
| rioxxterms.licenseref.startdate | 2024-04-16 | |
| rioxxterms.type | Journal Article/Review | en_GB |
| refterms.dateFCD | 2024-05-03T09:56:02Z | |
| refterms.versionFCD | VoR | |
| refterms.dateFOA | 2024-05-03T10:01:25Z | |
| refterms.panel | B | en_GB |
| refterms.dateFirstOnline | 2024-04-16 |
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copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.