FUNDAMENTAL GROUPS OF ALGEBRAIC STACKS
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(Received June 25 2002)
(Accepted November 6 2002)
Key Words: orbifold fundamental group; uniformization of stacks; fundamental group of coarse moduli.