Moduli spaces of fundamental groups in positive characteristic
In the 1980s, A. Grothendieck suggested a theory of arithmetic geometry called "anabelian geometry". This theory focuses on the following fundamental question: How much information about algebraic varieties can be carried by their algebraic fundamental groups? The conjectures based on this question are called Grothendieck's anabelian conjectures which have been studied deeply when the base fields are arithmetic (e.g. number fields, p-adic fields, finite fields, etc.) since the 1990s, and the non-trivial Galois representations play vital roles.
On the other hand, in 1996, A. Tamagawa discovered surprisingly that anabelian phenomena also exist for curves over algebraically closed fields of characteristic p>0 (i.e., no Galois actions). In this talk, I will explain these kinds of anabelian phenomena from the point of view of "moduli spaces of fundamental groups" introduced by the speaker, which gives a general framework for describing the anabelian phenomena for curves over algebraically closed fields of characteristic p.