北大数論セミナー：The Finite-Step Solvability of Anabelian Geometry

Time： 15:00 – 16:00

Place：理学部3号館3-307室　　　

Speaker：山口 永悟 氏（東京科学大）

Title： The Finite-Step Solvability of Anabelian Geometry

Abstract：The important conjecture in anabelian geometry, the Grothendieck conjecture, states a connection between the geometric properties of hyperbolic curves and the group-theoretic properties of their arithmetic fundamental groups, and has been proved by H. Nakamura, A. Tamagawa, and S. Mochizuki.
Our focus will be on one of the extensions of this conjecture, the $m$-step solvable Grothendieck conjecture, which states that we can reconstruct the geometric properties of hyperbolic curves from the maximal geometrically $m$-step solvable quotient of their arithmetic fundamental groups group-theoretically. In this talk, we will introduce the details of the $m$-step solvable Grothendieck conjecture and its proof obtained by the speaker, with a focusing on the case where the genus is $0$.

Organizer：朝倉 政典、安田 正大