On fields of totally $S$-adic numbers
Lior Bary-Soroker, Arno Fehm, with appendix by Florian Pop
TL;DR
This paper proves that the field of totally $S$-adic algebraic numbers, associated with a finite set of places of a number field, does not possess the Hilbertian property, impacting number theory and field theory.
Contribution
It establishes that the field of totally $S$-adic algebraic numbers is not Hilbertian, a novel result in the study of such fields.
Findings
The field of totally $S$-adic algebraic numbers is not Hilbertian.
The result applies to any finite set of places of a number field.
This influences the understanding of field properties in algebraic number theory.
Abstract
Given a finite set of places of a number field, we prove that the field of totally -adic algebraic numbers is not Hilbertian.
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Taxonomy
Topicsadvanced mathematical theories