Publications of the Research Institute for Mathematical Sciences
Full-Text PDF (545 KB) | Metadata | Table of Contents | PRIMS summary
Published online: 2018-07-23
On the Admissible Fundamental Groups of Curves over Algebraically Closed Fields of Characteristic $p > 0$Yu Yang (1) Kyoto University, Japan
In the present paper, we study the anabelian geometry of pointed stable curves over algebraically closed fields of positive characteristic. We prove that the semi-graph of anabelioids of PSC-type arising from a pointed stable curve over an algebraically closed field of positive characteristic can be reconstructed group-theoretically from its fundamental group. This result may be regarded as a version of the combinatorial Grothendieck conjecture in positive characteristic. As an application, we prove that if a pointed stable curve over an algebraic closure of a finite field satisfies certain conditions, then the isomorphism class of the admissible fundamental group of the pointed stable curve completely determines the isomorphism class of the pointed stable curve as a scheme. This result generalizes a result of A. Tamagawa to the case of (possibly singular) pointed stable curves.
Keywords: Positive characteristic, pointed stable curve, admissible fundamental group, semi-graph of anabelioids, anabelian geometry
Yang Yu: On the Admissible Fundamental Groups of Curves over Algebraically Closed Fields of Characteristic $p > 0$. Publ. Res. Inst. Math. Sci. 54 (2018), 649-678. doi: 10.4171/PRIMS/54-3-4