Publications of the Research Institute for Mathematical Sciences

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Volume 54, Issue 4, 2018, pp. 781–853
DOI: 10.4171/PRIMS/54-4-3

Published online: 2018-10-18

Pro-$p$ Grothendieck Conjecture for Hyperbolic Polycurves

Koichiro Sawada[1]

(1) Kyoto University, Japan

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

Keywords: Pro-$p$ Grothendieck conjecture, hyperbolic polycurve

Sawada Koichiro: Pro-$p$ Grothendieck Conjecture for Hyperbolic Polycurves. Publ. Res. Inst. Math. Sci. 54 (2018), 781-853. doi: 10.4171/PRIMS/54-4-3