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

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 ètale 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 ètale 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