Artin–Schreier quandles of involutions in absolute Galois groups
Abstract
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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Mathematical Identities
Polynomial and algebraic computation
Publication details
- Journal / source
- Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
- Publisher
- Springer Science and Business Media LLC
- Volume
- 96
- Issue
- 1
- Pages
- 1–21
- Publication date
- 1 April 2026
- Language
- EN