Advanced Topics in the Arithmetic of Elliptic Curves

✍ Scribed by Joseph H. Silverman (auth.)

Publisher: Springer-Verlag New York
Year: 1994
Tongue: English
Leaves: 540
Series: Graduate Texts in Mathematics 151
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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 additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.

✦ Table of Contents

Front Matter....Pages i-xiii
Introduction....Pages 1-4
Elliptic and Modular Functions....Pages 5-94
Complex Multiplication....Pages 95-186
Elliptic Surfaces....Pages 187-288
The Néron Model....Pages 289-407
Elliptic Curves over Complete Fields....Pages 408-453
Local Height Functions....Pages 454-480
Back Matter....Pages 481-528

✦ Subjects

Algebraic Geometry; Number Theory

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