Fundamental Groups of Algebraic Stacks

Details Fundamental Groups of Algebraic Stacks Fundamental Groups of Algebraic Stacks

2002-01-04

arxiv.org/abs/math/0201021v1

Mathematics

Algebraic Geometry

31 pages

Scientific paper

We study fundamental groups of algebraic stacks. We show that these fundamental groups carry an additional structure coming from the inertia groups. Then use this additional structure to analyze geometric/ topological properties of stacks. We give an explicit formula for the fundamental group of the coarse moduli space. Also, we use these additional structures to give a necessary and sufficient for an algebraic stack to be uniformizable.

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