Vol. 9, No. 5, 2015

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Homotopy exact sequences and orbifolds

Kentaro Mitsui

Vol. 9 (2015), No. 5, 1089–1136
Abstract

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

Keywords
orbifolds, elliptic surfaces, coverings of curves, étale fundamental groups, homotopy exact sequences, simply connected
Mathematical Subject Classification 2010
Primary: 14F35
Secondary: 14D06, 14J27, 14H30
Milestones
Received: 8 October 2014
Revised: 21 January 2015
Accepted: 11 March 2015
Published: 21 June 2015
Authors
Kentaro Mitsui
Department of Mathematics
Graduate School of Science
Kobe University
Hyogo 657-8501
Japan