Joseph H. Silverman (auth.)9780387943251, 9780387943282, 0387943250, 0387943285, 3540943250, 3540943285
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 |
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