Néron Models

  • Siegfried Bosch
  • Werner Lütkebohmert
  • Michel Raynaud
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 21)

Table of contents

  1. Front Matter
    Pages I-X
  2. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 1-5
  3. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 6-30
  4. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 31-59
  5. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 60-93
  6. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 94-111
  7. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 112-128
  8. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 129-171
  9. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 172-198
  10. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 199-235
  11. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 236-288
  12. Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
    Pages 289-316
  13. Back Matter
    Pages 317-328

About this book

Introduction

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.

Keywords

Abelsche Varietäten Algebra Algebraische Gruppen Arithmetic Invariant Jacobi-Varietäten Picard-Functor geometry proof theorem

Authors and affiliations

  • Siegfried Bosch
    • 1
  • Werner Lütkebohmert
    • 1
  • Michel Raynaud
    • 2
  1. 1.Mathematisches InstitutWestfälische Wilhelms-UniversitätMünsterGermany
  2. 2.Université de Paris-SudOrsayFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-51438-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08073-9
  • Online ISBN 978-3-642-51438-8
  • Series Print ISSN 0071-1136