On topological and combinatorial structures of pointed stable curves over algebraically closed fields of positive characteristic

Abstract

AbstractIn this paper, we study anabelian geometry of curves over algebraically closed fields of positive characteristic. Let be a pointed stable curve over an algebraically closed field of characteristic and the admissible fundamental group of . We prove that there exists a group‐theoretical algorithm, whose input datum is the admissible fundamental group , and whose output data are the topological and the combinatorial structures associated with . This result can be regarded as a mono‐anabelian version of the combinatorial Grothendieck conjecture in the positive characteristic. Moreover, by applying this result, we construct clutching maps for moduli spaces of admissible fundamental groups.