JournalsprimsVol. 54, No. 4pp. 781–853

Pro-pp Grothendieck Conjecture for Hyperbolic Polycurves

  • Koichiro Sawada

    Kyoto University, Japan
Pro-$p$ Grothendieck Conjecture for Hyperbolic Polycurves cover

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Abstract

In the present paper, we study the geometrically pro-pp 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 4\leq 4 over a sub-pp-adic field satisfying a certain group-theoretic condition is completely determined by the geometrically pro-pp fundamental group equipped with surjection onto the absolute Galois group of the base fi eld.

Cite this article

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

DOI 10.4171/PRIMS/54-4-3