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math.NT2026
Ab-faithfulness of absolute Galois groups in number theory
Naganori Yamaguchi
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 d…
math.NT2025
Étale fundamental groups of smooth arithmetic surfaces and the Grothendieck conjecture
Ryoji Shimizu, Naganori Yamaguchi
We study the structure of the étale fundamental groups of smooth curves over certain arithmetic schemes, and investigate the relative version of Grothendieck's anabelian conjecture…
math.NT2025
Symmetries of spaces and numbers -- anabelian geometry
Benjamin Collas, Takahiro Murotani, Naganori Yamaguchi
``Can number and geometric spaces be reconstructed from their symmetries?'' This question, which is at the heart of anabelian geometry, a theory built on the collaborative efforts…