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Article Dans Une Revue Annales Mathématiques Blaise Pascal Année : 2002

Theoreme de Van Kampen pour les champs algebriques

Résumé

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).

Dates et versions

hal-00007710 , version 1 (27-07-2005)

Identifiants

Citer

V. Zoonekynd. Theoreme de Van Kampen pour les champs algebriques. Annales Mathématiques Blaise Pascal, 2002, 97, pp.101-145. ⟨hal-00007710⟩
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