Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Yamaguchi, Naganori
Institution: Tokyo Denki University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220721089