Champs Algébriques

By: GÃ©rard Laumon, L. Moret-Bailly

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Hardcover | 1 November 1999

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Hardcover
224 Pages

Dimensions(cm)
23.5 x 15.88 x 1.27

Language
French

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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.

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La catégorie des S-espaces et sa sous-catégorie strictement pleine des S-espaces algébriques	p. 1
La 2-catégorie des S-groupoïdes	p. 7
La sous 2-catégorie strictement pleine des S-champs dans (Gr/S)	p. 15
La 2-catégorie des S-champs algébriques	p. 25
Points d'un S-champ algébrique; topologie de Zariski	p. 39
Quelques résultats de structure locale	p. 47
Critéres valuatifs; morphismes universellement fermés, morphismes séparés, morphismes propres	p. 59
Caractérisation des espaces algébriques et des champs de Deligne-Mumford	p. 73
Parenthése sur les topologies plates	p. 77
Les critéres d'Artin pour qu'un S-champ soit algébrique	p. 81
Points algébriques, faisceaux résiduels, gerbes résiduelles, dimension	p. 93
Faisceaux sur le site lisse-étale d'un S-champ algébrique	p. 101
Modules quasi-cohérents sur un S-champ algébrique	p. 119
Constructions locales	p. 133
Modules cohérents sur les S-champs algébriques localement noethériens	p. 145
Le théorème principal de Zariski. Applications à la structure globale des champs de Deligne-Mumford	p. 151
Le complexe cotangent d'un 1-morphisme de champs algébriques	p. 157
Faisceaux constructibles sur un S-champ algébrique	p. 175
Quelques prolongements	p. 193
Appendice compléments sur les espaces algébriques	p. 197
Bibliographie	p. 201
Index terminologique	p. 205
Table of Contents provided by Publisher. All Rights Reserved.

Champs Algébriques

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