Publications of the Research Institute for Mathematical Sciences


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Volume 54, Issue 3, 2018, pp. 649–678
DOI: 10.4171/PRIMS/54-3-4

Published online: 2018-07-23

On the Admissible Fundamental Groups of Curves over Algebraically Closed Fields of Characteristic $p > 0$

Yu Yang[1]

(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 fi eld 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 fi eld satisfi es 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