Advanced Topics in the Arithmetic of Elliptic Curves

Advanced Topics in the Arithmetic of Elliptic Curves
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
Total Pages: 482
Release: 2013-12-01
Genre: Mathematics
ISBN: 1461208513

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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.


Advanced Topics in the Arithmetic of Elliptic Curves
Language: en
Pages: 482
Authors: Joseph H. Silverman
Categories: Mathematics
Type: BOOK - Published: 2013-12-01 - Publisher: Springer Science & Business Media

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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, va
The Arithmetic of Elliptic Curves
Language: en
Pages: 414
Authors: Joseph H. Silverman
Categories: Mathematics
Type: BOOK - Published: 2013-03-09 - Publisher: Springer Science & Business Media

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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 ar
Rational Points on Elliptic Curves
Language: en
Pages: 292
Authors: Joseph H. Silverman
Categories: Mathematics
Type: BOOK - Published: 2013-04-17 - Publisher: Springer Science & Business Media

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The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic the
The Arithmetic of Elliptic Curves
Language: en
Pages: 525
Authors: Joseph H. Silverman
Categories: Mathematics
Type: BOOK - Published: 2009-04-20 - Publisher: Springer Science & Business Media

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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 ar
Elliptic Curves and Arithmetic Invariants
Language: en
Pages: 464
Authors: Haruzo Hida
Categories: Mathematics
Type: BOOK - Published: 2013-06-13 - Publisher: Springer Science & Business Media

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This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invari