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Advanced Topics in the Arithmetic of Elliptic Curves

✍ Scribed by Joseph H. Silverman

Publisher
Springer
Year
1999
Tongue
English
Leaves
536
Series
Graduate Texts in Mathematics
Category
Library
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✦ Synopsis

In 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 book continues the study of elliptic curves by presenting six important, but 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. NΓ©ron 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. NΓ©ron's theory of canonical local height functions.

πŸ“œ SIMILAR VOLUMES

Advanced Topics in the Arithmetic of Ell
πŸ“ Advanced Topics in the Arithmetic of Elliptic Curves
✍ Joseph H. Silverman (auth.) πŸ“‚ Library πŸ“… 1994 πŸ› Springer-Verlag New York 🌐 English

<p>In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additi

Advanced Topics in the Arithmetic of Ell
πŸ“ Advanced Topics in the Arithmetic of Elliptic Curves
✍ Joseph H. Silverman (auth.) πŸ“‚ Library πŸ“… 1994 πŸ› Springer-Verlag New York 🌐 English

<p>In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additi

Advanced topics in the arithmetic of ell
πŸ“ Advanced topics in the arithmetic of elliptic curves
✍ Joseph H. Silverman πŸ“‚ Library πŸ“… 1994 πŸ› Springer-Verlag 🌐 English

This book is meant to be an introductory text, albeit at an upper graduate level. The main prerequisite for reading this book is some familiarity with the basic theory of elliptic curves as described, for example, in the first volume. Numerous exercises have been included at the end of each ch

Advanced Topics in the Arithmetic of Ell
πŸ“ Advanced Topics in the Arithmetic of Elliptic Curves
✍ Joseph H. Silverman πŸ“‚ Library πŸ“… 1994 πŸ› Springer 🌐 English

This book is meant to be an introductory text, albeit at an upper graduate level. The main prerequisite for reading this book is some familiarity with the basic theory of elliptic curves as described, for example, in the first volume. Numerous exercises have been included at the end of each chapter.

The Arithmetic of Elliptic Curves
πŸ“ The Arithmetic of Elliptic Curves
✍ Joseph H. Silverman (auth.) πŸ“‚ Library πŸ“… 2009 πŸ› Springer-Verlag New York 🌐 English

<p><P>The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry.