The Fundamental Group of an Algebraic Stack

2001/11/07 by V. Zoonekynd, Zoonekynd, V.
Mathematics · #14F35 (primary) 14A20 18B25 20L05 18D05 (secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14A20 #msc:14F35 #msc:18B25 #msc:18D05 #msc:20L05

paper · pdf · doi:10.48550/arxiv.math/0111071

latex2e with xypic, 15 pages

arxiv created 2001/11/07 · arxiv updated 2009/11/30

Abstract

We define the notion of fundamental group of an algebraic stack, prove a comparison theorem between the fundamental group of a stack over the complex numbers and that of the associated analytic orbifold, show that this notion coincides with that defined with simplicial schemes by Oda and finally prove some short exact sequences involving these groups.

Related

• Fundamental Groups of Algebraic Stacks
• On the algebraic fundamental groups
• The Nori fundamental gerbe of tame stacks
• Algebraic fundamental group and simplicial complexes
• Loops on schemes and the algebraic fundamental group