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Arithmetic Algebraic Geometry

  • G. van der Geer
  • F. Oort
  • J. Steenbrink

Part of the Progress in Mathematics book series (PM, volume 89)

Table of contents

  1. Front Matter
    Pages i-x
  2. Gerard van der Geer, Frans Oort, Jozef Steenbrink
    Pages 1-2
  3. T. Chinburg, R. Rumely
    Pages 3-24
  4. Torsten Ekedahl, Bert Van Geemen
    Pages 51-74
  5. J. Franke
    Pages 75-152
  6. Johan De Jong, Rutger Noot
    Pages 177-192
  7. Frans Oort
    Pages 247-284
  8. A. N. Parshin
    Pages 285-292
  9. Kenneth A. Ribet
    Pages 293-307
  10. Karl Rubin
    Pages 309-324
  11. Back Matter
    Pages 445-446

About this book

Introduction

Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps.

Inspired by these exciting developments, the editors organized a meeting at Texel in 1989 and invited a number of mathematicians to write papers for this volume. Some of these papers were presented at the meeting; others arose from the discussions that took place. They were all chosen for their quality and relevance to the application of algebraic geometry to arithmetic problems.

Topics include: arithmetic surfaces, Chjerm functors, modular curves and modular varieties, elliptic curves, Kolyvagin’s work, K-theory and Galois representations. Besides the research papers, there is a letter of Parshin and a paper of Zagier with is interpretations of the Birch-Swinnerton-Dyer Conjecture.

Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.

Keywords

Algebraic K-theory Arithmetic Dimension Diophantine approximation Finite Grad K-theory Morphism algebra algebraic geometry equation function geometry number theory theorem

Editors and affiliations

  • G. van der Geer
    • 1
  • F. Oort
    • 2
  • J. Steenbrink
    • 3
  1. 1.Mathematisch InstituutUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.Mathematisch InstituutRijksuniversiteit UtrechtUtrechtThe Netherlands
  3. 3.Mathematisch InstituutKatholieke Universiteit NijmegenNijmegenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0457-2
  • Copyright Information Birkhäuser Boston, Inc. 1991
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6769-0
  • Online ISBN 978-1-4612-0457-2
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site