Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108

Nicholas M. Katz, Barry Mazur (Autoren)

Buch | Softcover

528 Seiten

1985
Princeton University Press (Verlag)
978-0-691-08352-0 (ISBN)

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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.

*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

Erscheint lt. Verlag	21.2.1985
Reihe/Serie	Annals of Mathematics Studies
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 229 mm
Gewicht	765 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-691-08352-5 / 0691083525
ISBN-13	978-0-691-08352-0 / 9780691083520
Zustand	Neuware