  Given two hyperbolic curves over p-adic local fields, the absolute anabelian
conjecture claims that any isomorphism between their \'etale fundamental group
comes from an isomorphism of schemes. This conjecture was proven by S.
Mochizuki for curves of quasi-Belyi type. The goal of this paper is to extend
the result to a wider family of curves, that includes for example hyperbolic
Mumford curves.
