Number Theory III

Diophantine Geometry

  • Serge Lang
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 60)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. R. V. Gamkrelidze
    Pages 1-42
  3. R. V. Gamkrelidze
    Pages 43-67
  4. R. V. Gamkrelidze
    Pages 68-100
  5. R. V. Gamkrelidze
    Pages 123-142
  6. R. V. Gamkrelidze
    Pages 143-162
  7. R. V. Gamkrelidze
    Pages 163-175
  8. R. V. Gamkrelidze
    Pages 176-204
  9. R. V. Gamkrelidze
    Pages 244-262
  10. Back Matter
    Pages 263-296

About this book

Introduction

From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments.

This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics are treated in a nice, coherent way, however not in a historically logical order. ...The author writes "At the moment of writing, the situation is in flux...". That is clear from the scope of this book. In the area described many conjectures, important results, new developments took place in the last 30 years. And still new results come at a breathtaking speed in this rich field. In the introduction the author notices: "I have included several connections of diophantine geometry with other parts of mathematics, such as PDE and Laplacians, complex analysis, and differential geometry. A grand unification is going on, with multiple connections between these fields." Such a unification becomes clear in this beautiful book, which we recommend for mathematicians of all disciplines." Medelingen van het wiskundig genootschap, 1994
"... It is fascinating to see how geometry, arithmetic and complex analysis grow together!..." Monatshefte für Mathematik, 1993

Keywords

Abelian varieties Abelian variety Dimension Diophantine approximation Divisor elliptic curve Isogenie number theory sheaves

Editors and affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-58227-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-61223-0
  • Online ISBN 978-3-642-58227-1
  • Series Print ISSN 0938-0396