arXiv subjects
Publications and source records attributed to V. Zoonekynd.
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.
The notion of tangencial base point is well-known for schemes in characteristic zero. We show that the definition in terms of Puiseux series generalizes to the case of Deligne--Mumford stacks, over a field of arbitrary characteristic. We then apply this construction to moduli spaces of smooth curves, generalizing a result of Ihara-Nakamura.
We define a category whose objects are finite etale coverings of an algebraic stack and prove that it is a Galois category and that it allows one to compute the fundamental group of the stack. We then prove a Van Kampen theorem for algebraic stacks whose simplest form reads: Let U and V be open substacks of an algebraic stack X with X = U \union V, let P be a set of base points, at least one in each connected component of X, U, V and U \inter V, then pi_1(X,P) is the amalgamated sum of pi_1(U,P) and pi_1(V,P) over pi_1(U \inter V, P).