Homotopy exact sequences and orbifolds

Kentaro Mitsui

We generalize the homotopy exact sequences of ├ętale fundamental groups for separable fibrations to the case where the fibrations are not necessarily separable. To treat the case where the fibrations admit non-reduced geometric fibers, we introduce orbifolds within the framework of schemes and study their fundamental groups. As an application, we give a criterion for simply connectedness of elliptic surfaces by classifying simply connected orbifold curves.