Synopsis
This book continues the treatment of the arithmetic theory of elliptic curves begun in the first volume. The book begins with the theory of elliptic and modular functions for the full modular group r(1), including a discussion of Hekcke operators and the L -series associated to cusp forms. This is followed by a detailed study of elliptic curves with complex multiplication, their associated Grössencharacters and L -series, and applications to the construction of abelian extensions of quadratic imaginary fields. Next comes a treatment of elliptic curves over function fields and elliptic surfaces, including specialization theorems for heights and sections. This material serves as a prelude to the theory of minimal models and Néron models of elliptic curves, with a discussion of special fibers, conductors, and Ogg's formula. Next comes a brief description of q -models for elliptic curves over C and R, followed by Tate's theory of q -models for elliptic curves with non-integral j -invariant over p -adic fields. The book concludes with the construction of canonical local height functions on elliptic curves, including explicit formulas for both archimedean and non-archimedean fields.
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..."this book deserves to be as popular as its forerunner and a great many people will be looking forward to reading a third volume." - Monatshefte fr Mathematik
.,."this book deserves to be as popular as its forerunner and a great many people will be looking forward to reading a third volume." - Monatshefte fA1/4r Mathematik
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Advanced Topics in the Arithmetic of Elliptic Curves (Graduate Texts in Mathematics). Joseph H. Silverman
Seller: ANTIQUARIAT Franke BRUDDENBOOKS, Lübeck, Germany
Seller rating 5 out of 5 stars
Broschur, 8°. Condition: Wie neu. 538 S. Buch ist neu, aus priv. Vorbesitz, ungelesen. -----Inhalt:. In the first volume of The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational points and Siegel's theorem on the finiteness of the set of integral points. This second volume continues the study of elliptic curves by presenting six important, somewhat more specialized topics: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Néron models, Kodaira-N ron classification of special fibres, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Néron's theory of canonical local height functions. From the contents: Preface Introduction Elliptic and Modular Functions Complex Multiplication Elliptic Surfaces The Neron Model Elliptic Curves over Complete Fields Local Height Functions Appendix A: Some Useful Tables Notes on Exercises References List of Notation Index. ISBN: 9783540943280 Wir senden umgehend mit beiliegender MwSt.Rechnung. Sprache: Englisch Gewicht in Gramm: 740. Seller Inventory # 669222