Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / Barry Mazur, Nicholas M. Katz.

Format:

Book

Author/Creator:

Katz, Nicholas M., author.

Mazur, Barry, author.

Series:

Annals of mathematics studies ; Number 108.

Annals of Mathematics Studies ; 272

Language:

English

Subjects (All):

Curves, Elliptic.

Moduli theory.

Geometry, Algebraic.

Physical Description:

1 online resource (532 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

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.

Contents:

Frontmatter

TABLE OF CONTENTS

INTRODUCTION

Chapter 1. GENERALITIES ON " A-STRUCTURES" AND " A-GENERATORS"

Chapter 2. REVIEW OF ELLIPTIC CURVES

Chapter 3. THE FOUR BASIC MODULI PROBLEMS FOR ELLIPTIC CURVES: SORITES

Chapter 4. THE FORMALISM OF MODULI PROBLEMS

Chapter 5. REGULARITY THEOREMS

Chapter 6. CYCLICITY

Chapter 7. QUOTIENTS BY FINITE GROUPS

Chapter 8. COARSE MODULI SCHEMES, CUSPS, AND COMPACTIFICATION

Chapter 9. MODULI PROBLEMS VIEWED OVER CYCLOTOMIC INTEGER RINGS

Chapter 10. THE CALCULUS OF CUSPS AND COMPONENTS VIA THE GROUPS T[N], AND THE GLOBAL STRUCTURE OF THE BASIC MODULI PROBLEMS

Chapter 11. INTERLUDE-EXOTIC MODULAR MORPHISMS AND ISOMORPHISMS

Chapter 12. NEW MODULI PROBLEMS IN CHARACTERISTIC p; IGUSA CURVES

Chapter 13. REDUCTIONS mod p OF THE BASIC MODULI PROBLEMS

Chapter 14. APPLICATION TO THEOREMS OF GOOD REDUCTION

NOTES ADDED IN PROOF

REFERENCES

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

Description based on publisher supplied metadata and other sources.

ISBN:

9781400881710

1400881714

OCLC:

979579083