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

• Autore: Katz Nicholas M.
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1985
• Descrizione fisica: 1 online resource (532 pages) : illustrations
• Disciplina: 516.3/5
• Soggetto topico: Curves, Elliptic; Moduli theory; Geometry, Algebraic
• Soggetto non controllato: Abelian variety; Addition; Algebraic variety; Algebraically closed field; Ambient space; Arithmetic; Axiom; Barry Mazur; Base change; Calculation; Canonical map; Change of base; Closed immersion; Coefficient; Coherent sheaf; Cokernel; Commutative property; Congruence relation; Coprime integers; Corollary; Cusp form; Cyclic group; Dense set; Diagram (category theory); Dimension; Discrete valuation ring; Disjoint union; Divisor; Eigenfunction; Elliptic curve; Empty set; Factorization; Field of fractions; Finite field; Finite group; Finite morphism; Free module; Functor; Group (mathematics); Integer; Irreducible component; Level structure; Local ring; Maximal ideal; Modular curve; Modular equation; Modular form; Moduli space; Morphism of schemes; Morphism; Neighbourhood (mathematics); Noetherian; One-parameter group; Open problem; Prime factor; Prime number; Prime power; Q.E.D.; Regularity theorem; Representation theory; Residue field; Riemann hypothesis; Smoothness; Special case; Subgroup; Subring; Subset; Theorem; Topology; Two-dimensional space; Zariski topology
• Persona (resp. second.): MazurBarry
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108
• ISBN: 1-4008-8171-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154753303321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 108.