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Rigid Geometry of Curves and Their Jacobians

  • Werner Lütkebohmert

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Werner Lütkebohmert
    Pages 1-28
  3. Werner Lütkebohmert
    Pages 29-101
  4. Werner Lütkebohmert
    Pages 103-175
  5. Werner Lütkebohmert
    Pages 177-216
  6. Werner Lütkebohmert
    Pages 217-254
  7. Werner Lütkebohmert
    Pages 255-308
  8. Werner Lütkebohmert
    Pages 309-353
  9. Back Matter
    Pages 355-386

About this book

Introduction

This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. 

Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.


Keywords

Algebraic Geometry Arithmetic Geometry Number Theory Several Complex Variables and Analytic Spaces Commutative Rings and Algebras

Authors and affiliations

  • Werner Lütkebohmert
    • 1
  1. 1.Institute of Pure MathematicsUlm UniversityUlmGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-27371-6
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-27369-3
  • Online ISBN 978-3-319-27371-6
  • Series Print ISSN 0071-1136
  • Series Online ISSN 2197-5655
  • Buy this book on publisher's site
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