On the Pro-$p$ Absolute Anabelian Geometry of Proper Hyperbolic Curves

J. Math. Sci. Univ. Tokyo
Vol. 25 (2018), No. 1, Page 1-34.

Hoshi, Yuichiro
On the Pro-$p$ Absolute Anabelian Geometry of Proper Hyperbolic Curves
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Abstract:
In the present paper, we study the geometry of the stable models of proper hyperbolic curves over $p$-adic local fields via the study of the geometrically pro-$p$ étale fundamental groups of the curves. In particular, we establish functorial “group-theoretic” algorithms for reconstructing various objects related to the geometry of stable models from the geometrically pro-$p$ étale fundamental groups. As an application, we also give a pro-$p$ “group-theoretic” criterion for good reduction of ordinary proper hyperbolic curves over $p$-adic local fields.

Keywords: hyperbolic curve, $p$-adic local field, ordinary, good reduction

Mathematics Subject Classification (14): 14H30
Mathematical Reviews Number: MR3790875

Received: 2016-10-20