Number Theory Seminar by Paul Helminck
Paul Helminck (Bremen) will give a Number Theory Seminar on Friday, January 11, in Aud 10 starting 14:15.
Title: Decompositions of tame fundamental groups of nonarchimedean curves using metrized complexes
Abstract: In this talk, I’ll discuss a natural functor from the category of tame étale coverings of a punctured nonarchimedean curve to the category of tame étale coverings of a metrized complex associated to the punctured curve. In its simplest form, this functor takes a covering of algebraic curves and assigns to it a covering of intersection graphs arising from a morphism of semistable models. By considering the enhanced category of coverings of metrized complexes with gluing data, we then show that we obtain an equivalence of categories, yielding a natural notion of a profinite fundamental group for metrized complexes since the categories involved are Galois categories.