分野別セミナー

[講演概要]
In Anabelian geometry, we have an important conjecture by A. Grothendieck, which states that the geometric properties of (algebraic) hyperbolic curves can be determined group-theoretically by studying their arithmetic fundamental groups. H. Nakamura, A. Tamagawa, and S. Mochizuki proved this conjecture for finitely generated fields over $\mathbb{Q}$. This talk focuses on one of the remaining problems related to this conjecture, called the $m$-step solvable Grothendieck conjecture, which concerns the group-theoretical reconstruction of geometric properties of hyperbolic curves by the maximal geometrically $m(\geq 2)$-step solvable quotient of their arithmetic fundamental groups. This talk will explain the $m$-step solvable Grothendieck conjecture and a part of its proof as obtained by the speaker, focusing on the case where $g=0$.