LAUSR

In the present paper, we study anabelian geometry of curves over algebraically closed fields of positive characteristic. Let X• = (X,DX) be a pointed stable curve over an algebraically closed field of characteristic p > 0 and ΠX• the admissible fundamental group of X•. We prove that there exists a group-theoretical algorithm whose input datum is the admissible fundamental group ΠX• , and whose output data are the topological and the combinatorial structures associated to X•. This result can be regarded as a mono-anabelian version of the combinatorial Grothendieck conjecture in positive characteristic. Moreover, by applying this result, we construct clutching maps for moduli spaces of admissible fundamental groups.