The absolute anabelian geometry of quasi-tripods

Abstract

— In the present paper, we study the absolute anabelian geometry of hyperbolic orbicurves. The first main result of the present paper shows the absolute version of the Grothendieck conjecture for quasi-tripods — e.g., hyperbolic curves of genus less than two — over, for instance, finitely generated extensions of mixed-characteristic local fields. Moreover, we prove some absolute anabelian results for certain hyperbolic polycurves as applications of the first main result. Finally, we also show the absolute version of the Grothendieck conjecture for MLF-isotrivial hyperbolic orbicurves over finitely generated extensions of mixedcharacteristic local fields.