| Advanced Topics in the Arithmetic of Elliptic Curves Softcover Repri Edition Contributor(s): Silverman, Joseph H. (Author) |
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ISBN: 0387943285 ISBN-13: 9780387943282 Publisher: Springer OUR PRICE: $66.49 Product Type: Paperback - Other Formats Published: November 1994 Annotation: 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 Gr??ssencharacters 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 N??ron 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Algebraic - Mathematics | Algebra - General |
| Dewey: 516.352 |
| LCCN: 94021787 |
| Series: Graduate Texts in Mathematics |
| Physical Information: 1.16" H x 6.34" W x 9.2" (1.68 lbs) 528 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
