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<p>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.</p>

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Artin–Schreier quandles of involutions in absolute Galois groups

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  • 发表日期：

    2026年5月6日

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  • Markus Szymik

摘要

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.