Theoreme de Van Kampen pour les champs algebriques

Abstract

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).