The m-step solvable anabelian geometry for hyperbolic curves over finitely generated fields

Abstract: In anabelian geometry, there is a conjecture, called Grothendieck's conjecture (i.e. can we reconstruct group-theoretically a hyperbolic curve from its etale fundamental group?). This conjecture has been solved in the affirmative in many cases. Regarding this conjecture, if we replace the fundamental group with its maximal m-step solvable quotient, then does the conjecture still hold? (Write m-GC for this question). m-GC has rarely been proved, and we only have three previous studies (Nakamura, Mochizuki). In this talk, I explain the content of these conjectures and of the previous studies. In particular, I explain a recent result that solves m-GC for affine hyperbolic curves over finitely generated fields.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October