Pro- Grothendieck Conjecture for Hyperbolic Polycurves
Koichiro Sawada
Kyoto University, Japan
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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