Arithmetic Moduli of Elliptic Curves
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.

1121850408
Arithmetic Moduli of Elliptic Curves
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.

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Arithmetic Moduli of Elliptic Curves

Arithmetic Moduli of Elliptic Curves

by Nicholas M. Katz, Barry Mazur
Arithmetic Moduli of Elliptic Curves

Arithmetic Moduli of Elliptic Curves

by Nicholas M. Katz, Barry Mazur

Overview

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.

Product Details

ISBN-13: 9780691083520
Publisher: Princeton University Press
Publication date: 02/21/1985
Series: Annals of Mathematics Studies , #108
Pages: 528
Product dimensions: 6.00(w) x 9.00(h) x (d)

Table of Contents

  • Frontmatter, pg. i
  • TABLE OF CONTENTS, pg. v
  • INTRODUCTION, pg. ix
  • Chapter 1. GENERALITIES ON “ A-STRUCTURES” AND “ A-GENERATORS”, pg. 1
  • Chapter 2. REVIEW OF ELLIPTIC CURVES, pg. 63
  • Chapter 3. THE FOUR BASIC MODULI PROBLEMS FOR ELLIPTIC CURVES: SORITES, pg. 98
  • Chapter 4. THE FORMALISM OF MODULI PROBLEMS, pg. 107
  • Chapter 5. REGULARITY THEOREMS, pg. 129
  • Chapter 6. CYCLICITY, pg. 152
  • Chapter 7. QUOTIENTS BY FINITE GROUPS, pg. 186
  • Chapter 8. COARSE MODULI SCHEMES, CUSPS, AND COMPACTIFICATION, pg. 224
  • Chapter 9. MODULI PROBLEMS VIEWED OVER CYCLOTOMIC INTEGER RINGS, pg. 271
  • Chapter 1 . THE CALCULUS OF CUSPS AND COMPONENTS VIA THE GROUPS T[N], AND THE GLOBAL STRUCTURE OF THE BASIC MODULI PROBLEMS, pg. 286
  • Chapter 11. INTERLUDE-EXOTIC MODULAR MORPHISMS AND ISOMORPHISMS, pg. 339
  • Chapter 12. NEW MODULI PROBLEMS IN CHARACTERISTIC p; IGUSA CURVES, pg. 344
  • Chapter 13. REDUCTIONS mod p OF THE BASIC MODULI PROBLEMS, pg. 389
  • Chapter 14. APPLICATION TO THEOREMS OF GOOD REDUCTION, pg. 457
  • NOTES ADDED IN PROOF, pg. 505
  • REFERENCES, pg. 511



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