Artin-Schreier quandles of involutions in absolute Galois groups
arXiv:2403.07545 · doi:10.1007/s12188-026-00297-z
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 formally real number fields, it is freely generated in its variety 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 and other examples show that, in general, there are relations.
22 pages, 1 figure, to appear in Abh. Math. Sem. Univ. Hamburg