Pro-p and cohomological aspects of anabelian geometry of hyperbolic polycurves (Algebraic Number Theory and Related Topics 2016)

Abstract

In this article, we study the étale fundamental groups of hyperbolic polycurves, i.e., successive extensions of families of hyperbolic curves. Among others, we show that the isomorphism class of a hyperbolic polycurve of dimension ≤ 4 defined over a sub-p-adic field is completely determined by its geometrically pro-p fundamental group under a certain group-theoretic condition. Moreover, we show that the dimension of a hyperbolic polycurve over a field of characteristic zero can be reconstructed group-theoretically from its geometric fundamental group. This article is based on author's works [11], [12].