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Champs algébriques

  • Book
  • © 2000

Overview

Authors:
  1. Gérard Laumon

    1. Mathématique, UMR 8628, CNRS et Université de Paris-Sud, Orsay, Cedex, France

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  2. Laurent Moret-Bailly

    1. IRMAR, UMR 6625, Université de Rennes 1, Rennes, Cedex, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • A "must" for every library and for all algebraic geometers, even if their knowledge of French is only basic
  • The first systematic account of the general theory of algebraic stacks over an arbitrary base scheme
  • Covers the basic definitions and constructions, but also new topics such as the "lisse-étale" topology
  • Includes supplementary material: sn.pub/extras

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. La catégorie des S-espaces et sa sous-catégorie strictement pleine des S-espaces algébriques

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 1-5

  3. La 2-catégorie des S-groupoïdes

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 7-13

  4. La sous 2-catégorie strictement pleine des S-champs dans (Gr/S)

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 15-24

  5. La 2-catégorie des S-champs dans algébriques

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 25-38

  6. Points d’un S-champ algébrique; topologie de Zariski

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 39-46

  7. Quelques résultats de structure locale

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 47-58

  8. Critères valuatifs; morphismes universellement fermés, morphismes séparés, morphismes propres

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 59-72

  9. Caractérisation des espaces algébriques et des champs de Deligne-Mumford

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 73-75

  10. Parenthèse sur les topologies plates

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 77-79

  11. Les critères d’Artin pour qu’un S-champ soit algébrique

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 81-91

  12. Points algébriques, faisceaux résiduels, gerbes résiduelles, dimension

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 93-100

  13. Faisceaux sur le site lisse-étale d’un S-champ algébrique

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 101-117

  14. Modules quasi-cohérents sur un Schamp algébrique

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 119-131

  15. Constructions locales

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 133-143

  16. Modules cohérents sur les S-champs algébriques localement noethériens

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 145-149

  17. Le théoremè principal de Zariski. Applications à la structure globale des champs de Deligne-Mumford

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 151-155

  18. Le complexe cotangent d’un 1-morphisme de champs algébriques

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 157-174

  19. Faisceaux constructibles sur un S-champ algébrique

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 175-192

  20. Quelques prolongements

    • Gérard Laumon, Laurent Moret-Bailly
    Pages 193-196
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Keywords

About this book

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.

Authors and Affiliations

  • Mathématique, UMR 8628, CNRS et Université de Paris-Sud, Orsay, Cedex, France

    Gérard Laumon

  • IRMAR, UMR 6625, Université de Rennes 1, Rennes, Cedex, France

    Laurent Moret-Bailly

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