On the averages of generalized Hasse-Witt invariants of pointed stable curves in positive characteristic

摘要

In the present paper, we study fundamental groups of curves in positive characteristic. Let X center dot be a pointed stable curve of type (gX,nX) over an algebraically closed field of characteristic p>0, Gamma X center dot the dual semi-graph of X center dot, and pi X center dot the admissible fundamental group of X center dot. In the present paper, we study a kind of group-theoretical invariant Avrp(pi X center dot){Avr}_{p}(Pi _{X<^>{ullet }})$$end{document} associated to the isomorphism class of pi X center dot called the limit of p-averages of pi X center dot, which plays a central role in the theory of anabelian geometry of curves over algebraically closed fields of positive characteristic.