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Néron Models

  • Book
  • © 1990

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Authors:
  1. Siegfried Bosch

    1. Mathematisches Institut, Westfälische Wilhelms-Universität, Münster, Germany

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  2. Werner Lütkebohmert

    1. Mathematisches Institut, Westfälische Wilhelms-Universität, Münster, Germany

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  3. Michel Raynaud

    1. Université de Paris-Sud, Orsay, France

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 1-5

  3. What Is a Néron Model?

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 6-30

  4. Some Background Material from Algebraic Geometry

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 31-59

  5. The Smoothening Process

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 60-93

  6. Construction of Birational Group Laws

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 94-111

  7. From Birational Group Laws to Group Schemes

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 112-128

  8. Descent

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 129-171

  9. Properties of Néron Models

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 172-198

  10. The Picard Functor

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 199-235

  11. Jacobians of Relative Curves

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 236-288

  12. Néron Models of Not Necessarily Proper Algebraic Groups

    • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 289-316

  13. Back Matter

    Pages 317-328
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Keywords

About this book

Néron models were invented by A. Néron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of Néron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Néron models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of Néron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Néron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between Néron models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor.

Authors and Affiliations

  • Mathematisches Institut, Westfälische Wilhelms-Universität, Münster, Germany

    Siegfried Bosch, Werner Lütkebohmert

  • Université de Paris-Sud, Orsay, France

    Michel Raynaud

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