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Introduction to Arakelov Theory

  • Serge Lang

Table of contents

  1. Front Matter
    Pages i-x
  2. Serge Lang
    Pages 1-19
  3. Serge Lang
    Pages 102-130
  4. Serge Lang
    Pages 131-154
  5. Back Matter
    Pages 155-187

About this book

Introduction

Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field. The book gives an introduction to this theory, including the analogues of the Hodge Index Theorem, the Arakelov adjunction formula, and the Faltings Riemann-Roch theorem. The book is intended for second year graduate students and researchers in the field who want a systematic introduction to the subject. The residue theorem, which forms the basis for the adjunction formula, is proved by a direct method due to Kunz and Waldi. The Faltings Riemann-Roch theorem is proved without assumptions of semistability. An effort has been made to include all necessary details, and as complete references as possible, especially to needed facts of analysis for Green's functions and the Faltings metrics.

Keywords

Divisor Grad Riemann-Roch theorem cohomology field

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1031-3
  • Copyright Information Springer-Verlag New York Inc. 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6991-5
  • Online ISBN 978-1-4612-1031-3
  • Buy this book on publisher's site