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FUNDAMENTAL GROUPS OF ALGEBRAIC STACKS

Published online by Cambridge University Press:  27 January 2004

B. Noohi
B. Noohi
Affiliation:
Department of Mathematics, Middlesex College, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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Abstract

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We study the fundamental groups of algebraic stacks. We show that these fundamental groups carry an additional structure coming from the inertia groups. We use this additional structure to analyse geometric/topological properties of stacks. We give an explicit formula for the fundamental group of the coarse moduli space. As an application, we find an explicit formula for the fundamental group of the geometric quotient of an arbitrary algebraic group action. Also, we use these additional structures to give a necessary and sufficient for an algebraic stack to be uniformizable (i.e. quotient of an algebraic space by a finite group action).

AMS 2000 Mathematics subject classification: Primary 14A20. Secondary 14F35; 14L30

Keywords

orbifold fundamental groupuniformization of stacksfundamental group of coarse moduli
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 3 , Issue 1 , January 2004 , pp. 69 - 103
Copyright
2004 Cambridge University Press