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Extension of solvable coverings across horizontal divisors over the integers
Naganori Yamaguchi
We study the effect of deleting a horizontal divisor from an arithmetic scheme on its étale fundamental group. Assume that the scheme is regular along the divisor, that each prime…
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…
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…
The metabelian Grothendieck conjecture for genus zero curves over finitely generated fields
Naganori Yamaguchi
In this paper, we prove the metabelian Grothendieck conjecture for genus-zero curves over finitely generated fields. More precisely, we show that two hyperbolic genus-zero curves a…
The geometrically m-step solvable Grothendieck conjecture for affine hyperbolic curves over finitely generated fields
Naganori Yamaguchi
In this paper, we present some new results on the geometrically m-step solvable Grothendieck conjecture in anabelian geometry. Specifically, we show the (weak bi-anabelian and stro…
A survey of known results on the m-step solvable anabelian geometry for hyperbolic curves
Naganori Yamaguchi
In this survey, we introduce the three theorems about the m-step solvable Grothendieck conjecture in anabelian geometry of hyperbolic curves by H. Nakamura, S. Mochizuki, and the a…
The geometrically m-step solvable Grothendieck conjecture for genus 0 curves over finitely generated fields
Naganori Yamaguchi
In this paper, we present some partial results for the geometrically m-step solvable Grothendieck conjecture in anabelian geometry. Among other things, we prove the geometrically 3…