Recent progress in higher-dimensional anabelian geometry (Algebraic Number Theory and Related Topics 2016)

Abstract

The purpose of this article is to report contents of the author's lecture delivered in the workshop "Algebraic Number Theory and Related Topics 2016" in Kyoto University. We survey some known facts about the Grothendieck conjecture for algebraic varieties of dimension greater than one, and then present the author's recent works on hyperbolic polycurves-algebraic varieties in the form of successive fiberations by hyperbolic curves. In particular, we focus on a certain hyperbolic polycurve obtained as a finite étale cover of M2, r, the moduli space of curves of genus two with ordered r marked points.