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Arithmetic Geometry

  • Book
  • © 1986

Overview

Editors:
  1. Gary Cornell

    1. Department of Mathematics, University of Connecticut, Storrs, USA

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  2. Joseph H. Silverman

    1. Department of Mathematics, Boston University, Boston, USA

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xv
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  2. Some Historical Notes

    • Gerd Faltings
    Pages 1-8

  3. Finiteness Theorems for Abelian Varieties over Number Fields

    • Gerd Faltings
    Pages 9-26

  4. Group Schemes, Formal Groups, and p-Divisible Groups

    • Stephen S. Shatz
    Pages 29-78

  5. Abelian Varieties over ℂ

    • Michael Rosen
    Pages 79-101

  6. Abelian Varieties

    • J. S. Milne
    Pages 103-150

  7. The Theory of Height Functions

    • Joseph H. Silverman
    Pages 151-166

  8. Jacobian Varieties

    • J. S. Milne
    Pages 167-212

  9. Néron Models

    • M. Artin
    Pages 213-230

  10. Siegel Moduli Schemes and Their Compactifications over ℂ

    • Ching-Li Chai
    Pages 231-251

  11. Heights and Elliptic Curves

    • Joseph H. Silverman
    Pages 253-265

  12. Lipman’s Proof of Resolution of Singularities for Surfaces

    • M. Artin
    Pages 267-287

  13. An Introduction to Arakelov Intersection Theory

    • T. Chinburg
    Pages 289-307

  14. Minimal Models for Curves over Dedekind Rings

    • T. Chinburg
    Pages 309-326

  15. Local Heights on Curves

    • Benedict H. Gross
    Pages 327-339

  16. A Higher Dimensional Mordell Conjecture

    • Paul Vojta
    Pages 341-353

  17. Erratum to: Erratum

    • Gary Cornell, Joseph H. Silverman
    Pages 354-354
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About this book

This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt­ ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation.

Editors and Affiliations

  • Department of Mathematics, University of Connecticut, Storrs, USA

    Gary Cornell

  • Department of Mathematics, Boston University, Boston, USA

    Joseph H. Silverman

Bibliographic Information

  • Book Title: Arithmetic Geometry

  • Editors: Gary Cornell, Joseph H. Silverman

  • DOI: https://doi.org/10.1007/978-1-4613-8655-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1986

  • Hardcover ISBN: 978-0-387-96311-2Published: 20 August 1986

  • Softcover ISBN: 978-1-4613-8657-5Published: 08 November 2011

  • eBook ISBN: 978-1-4613-8655-1Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XV, 353

  • Topics: Geometry

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