Abstract
In this paper, we study higher dimensional anabelian geometry. We prove the Grothendieck conjecture for certain types of hyperbolic polycurves (i.e., algebraic varieties in the form of successive fibrations by hyperbolic curves) over a sub-p-adic field (i.e., a field isomorphic to a subfield of a field finitely generated over the p-adic field Qp) for some prime number p. Among other things, we prove the Grothendieck conjecture for hyperbolic polycurves obtained as certain types of finite étale covers of the moduli space of curves of genus two with ordered r marked points over a sub-p-adic field.
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