Champs algbriques [Hardcover]

The theory of algebraic stacks emerged in the late sixties and early seventies in the works of P. Deligne, D. Mumford, and M. Artin. The language of algebraic stacks has been used repeatedly since then, mostly in connection with moduli problems: the increasing demand for an accurate description of moduli spaces came from various areas of mathematics and mathematical physics. Unfortunately the basic results on algebraic stacks were scattered in the literature and sometimes stated without proofs. The aim of this book is to fill this reference gap by providing mathematicians with the first systematic account of the general theory of (quasiseparated) algebraic stacks over an arbitrary base scheme. It covers the basic definitions and constructions, techniques for extending scheme-theoretic notions to stacks, Artin's representability theorems, but also new topics such as the lisse-?tale topology.Introduction.- La cat?gorie des S-espaces et sa sous-cat?gorie strictement pleine des S-espaces alg?briques.-La 2-cat?gorie des S-groupoides.-La sous-2-cat?gorie strictement pleine des S-champs dans (Gr/S).-La 2-cat?gorie des S-champs alg?briques.-Points d'un S-champ alg?brique; topologie de Zariski.-Quelques r?sultats de structure locale.-Crit?res valuatifs; morphismes universellement ferm?s, morphismes s?par?s, morphismes propres.-Caract?risation des espaces alg?briques et des champs de Deligne-Mumford.-Parenth?se sur les topologies plates.-Les crit?res d'Artin pour qu'un S-champ soit alg?brique.-Points alg?briques, faisceaux r?siduels, gerbes r?siduelles, dimension.-Faisceaux sur le site lisse-?tale d'un S-champ alg?brique.-Modules quasi-coh?rents sur un S-champ alg?brique.-Constructions locales.-Modules coh?rents sur les S-champs alg?briques localement noeth?riens.-Le th?or?me principal de Zariski. Applications ? la structure globale des champs de Deligne-Mumford.-Le complexe cotangent d'un 1-morphisme de champs alg?briques.-Faisceaux constructibles sur un S-champ alg?briql“Ü