Pro- Grothendieck Conjecture for Hyperbolic Polycurves

  • Koichiro Sawada

    Kyoto University, Japan

Abstract

In the present paper, we study the geometrically pro- fundamental groups of hyperbolic polycurves, i.e., successive extensions of families of hyperbolic curves. Among other results, we show that the isomorphism class of a hyperbolic polycurve of dimension over a sub--adic field satisfying a certain group-theoretic condition is completely determined by the geometrically pro- fundamental group equipped with surjection onto the absolute Galois group of the base field.

Cite this article

Koichiro Sawada, Pro- Grothendieck Conjecture for Hyperbolic Polycurves. Publ. Res. Inst. Math. Sci. 54 (2018), no. 4, pp. 781–853

DOI 10.4171/PRIMS/54-4-3