Szymik, M. orcid.org/0000-0002-7078-2699 (2026) Artin–Schreier quandles of involutions in absolute Galois groups. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. ISSN: 0025-5858
Abstract
We introduce a new invariant of fields that refines their real spectrum and is related to their absolute Galois group: the Artin–Schreier quandle. For totally real number fields, it is freely generated—in the variety of profinite involutory quandles—by a Cantor space of indeterminates. For Laurent series fields, we compute it in terms of the Artin–Schreier quandle of the coefficient field. This result, along with other examples, shows that, in general, there are relations.
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| Item Type: | Article |
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| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | © The Author(s) 2026. 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/. |
| Keywords: | Absolute Galois groups; Arithmetic topology; Artin–Schreier theory; Involutions; Quandles; Real spectra |
| Dates: |
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| Institution: | The University of Sheffield |
| Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
| Date Deposited: | 12 May 2026 07:37 |
| Last Modified: | 12 May 2026 07:37 |
| Status: | Published online |
| Publisher: | Springer Science and Business Media LLC |
| Refereed: | Yes |
| Identification Number: | 10.1007/s12188-026-00297-z |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:241001 |
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