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arXiv · 2610.05634

Ab-faithfulness of absolute Galois groups in number theory

Naganori Yamaguchi
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Abstract

We prove that the absolute Galois group of every discretely valued field of mixed characteristic is ab-faithful. We also prove ab-faithfulness for higher local fields of positive dimension and give further examples using finite split embedding problems. Finally, we give a formal Hilbert~90 criterion for center-freeness and slimness of finite-step solvable quotients. We apply this criterion to ab-faithful absolute Galois groups and obtain slimness for several classes of fields, including higher local fields of positive dimension.

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BibTeXRIS

Naganori Yamaguchi. 2026-10-04. Ab-faithfulness of absolute Galois groups in number theory. https://arxiv.org/abs/2610.05634

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