Work

The geometrically m$m$‐step solvable Grothendieck conjecture for affine hyperbolic curves over finitely generated fields

Year: 2024

Type: article

Abstract: In this paper, we present some new results on the geometrically ‐step solvable Grothendieck conjecture in anabelian geometry. Specifically, we show the (weak bianabelian and strong bianabelian) geometrically ‐step solvable Grothendieck conjecture(s) for affine hyperbolic curves over fields finitely generated over the prime field. First of all, we show the conjecture over finite fields. Next, we show the geometrically ‐step solvable version of the Oda–Tamagawa good reduction criterion for hyperbolic curves. Finally, by using these two results, we show the conjecture over fields finitely generated over the prime field.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.12912

Author: Naganori Yamaguchi

Institution: Tokyo Institute of Technology

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: On the m-step solvable Grothendieck conjecture in anabelian geometry