Arithmetic and Combinatorial Study of Anabelian Geometry

通过与望月新一的合作，我发展了组合anabel几何的基本理论。作为这一理论的应用，我和望月新一证明了Grothendieck的Anabelian猜想的几何版本的通用曲线的模堆栈的点曲线。在研究双曲曲线的单值充满度时，给出了拟单值充满度的l-独立性问题的一个反例。在研究数域上曲线的双有理截猜想时，得到了小数域上曲线的双有理Galois截是几何的一个充要条件.

By a joint work with Shinichi Mochizuki, I developed the fundamental theory of the combinatorial anabelian geometry. As an application of this theory, I and Shinichi Mochizuki proved a geometric version of Grothendieck's anabelian conjecture for the universal curve over the moduli stack of pointed curves. In the study of the monodromic fullness of hyperbolic curves, I gave a counter-example of the problem of the l-independency of quasi-monodromic fullness. In the study of the birational section conjecture for curves over number field, I obtained a necessary and sufficient condition for a birational Galois section of a curve over a small number field to be geometric.