Overview

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-étale"" topology.

Full Product Details

Author:   Gérard Laumon ,  L. Moret-Bailly
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2000 ed.
Volume:   39
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   1.090kg
ISBN:  

9783540657613

ISBN 10:   3540657614
Pages:   208
Publication Date:   22 November 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Language:   French

Table of Contents

Introduction.- La categorie des S-espaces et sa sous-categorie strictement pleine des S-espaces algebriques.-La 2-categorie des S-groupoides.-La sous-2-categorie strictement pleine des S-champs dans (Gr/S).-La 2-categorie des S-champs algebriques.-Points d'un S-champ algebrique; topologie de Zariski.-Quelques resultats de structure locale.-Criteres valuatifs; morphismes universellement fermes, morphismes separes, morphismes propres.-Caracterisation des espaces algebriques et des champs de Deligne-Mumford.-Parenthese sur les topologies plates.-Les criteres d'Artin pour qu'un S-champ soit algebrique.-Points algebriques, faisceaux residuels, gerbes residuelles, dimension.-Faisceaux sur le site lisse-etale d'un S-champ algebrique.-Modules quasi-coherents sur un S-champ algebrique.-Constructions locales.-Modules coherents sur les S-champs algebriques localement noetheriens.-Le theoreme principal de Zariski. Applications a la structure globale des champs de Deligne-Mumford.-Le complexe cotangent d'un 1-morphisme de champs algebriques.-Faisceaux constructibles sur un S-champ algebrique.-Quelques prolongements.-Appendice: complements sur les espaces algebriques. . ......

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