From the 1 of 6 linked papers with an AI index.
6 papers
On branched coverings of the projective line over the integers
Ryoji Shimizu, Naganori Yamaguchi
We investigate the étale fundamental group of the complement of a horizontal divisor on . We prove that this group has no nontrivial finite solvable qu…
The metabelian Grothendieck conjecture for genus zero curves over finitely generated fields
Naganori Yamaguchi
The paper proves that two hyperbolic genus‑zero curves over a finitely generated field are isomorphic (up to Frobenius twist in positive characteristic) exactly when their geometri…
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…
Center-freeness of finite-step solvable groups arising from anabelian geometry
Naganori Yamaguchi
Anabelian geometry suggests that, for suitably geometric objects, their étale fundamental groups determine the geometric objects up to isomorphism. From a group-theoretic viewpoin…
Anabelian geometry for Deligne-Mumford curves
Benjamin Collas, Séverin Philip, Naganori Yamaguchi
We develop an anabelian framework for general Deligne-Mumford curves, showing that their stack and orbifold structures are encoded in the group-theoretic properties of their étale…
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…