Arithmetic Moduli of Elliptic Curves
1st Edition
Published on 6. June 2016
528 pages
978-1-4008-8171-0 (ISBN)
Description
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.
More details
Other editions
Additional editions
Nicholas M. Katz | Barry Mazur
Arithmetic Moduli of Elliptic Curves
Book
02/1985
Princeton University Press
€112.10
Shipment within 10-20 days
Nicholas M. Katz | Barry Mazur
Arithmetic Moduli of Elliptic Curves
Book
02/1985
Princeton University Press
€80.47
Article exhausted; check different version
Persons
Nicholas M. Katz & Barry Mazur
Content
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
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
