Homotopy exact sequences and orbifolds

Kentaro Mitsui

We generalize the homotopy exact sequences of étale 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.