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Introduction to Arakelov Theory

  • Book
  • © 1988

Overview

Authors:
  1. Serge Lang

    1. Department of Mathematics, Yale University, New Haven, USA

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Metrics and Chern Forms

    • Serge Lang
    Pages 1-19

  3. Green’s Functions on Riemann Surfaces

    • Serge Lang
    Pages 20-47

  4. Intersections on an Arithmetic Surface

    • Serge Lang
    Pages 48-69

  5. Hodge Index Theorem and the Adjunction Formula

    • Serge Lang
    Pages 70-101

  6. The Faltings Riemann-Roch Theorem

    • Serge Lang
    Pages 102-130

  7. Faltings Volumes on Cohomology

    • Serge Lang
    Pages 131-154

  8. Back Matter

    Pages 155-187
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

Bibliographic Information

  • Book Title: Introduction to Arakelov Theory

  • Authors: Serge Lang

  • DOI: https://doi.org/10.1007/978-1-4612-1031-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1988

  • Hardcover ISBN: 978-0-387-96793-6Published: 09 November 1988

  • Softcover ISBN: 978-1-4612-6991-5Published: 30 September 2012

  • eBook ISBN: 978-1-4612-1031-3Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 187

  • Topics: Algebra

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