Share

Advanced Topics in the Arithmetic of Elliptic Curves

2013-12-01 Mathematics
Download Advanced Topics in the Arithmetic of Elliptic Curves PDF Online Free

Author :
Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 513/5 ( reviews)

GET EBOOK


Book Synopsis Advanced Topics in the Arithmetic of Elliptic Curves by : Joseph H. Silverman

Download or read book Advanced Topics in the Arithmetic of Elliptic Curves written by Joseph H. Silverman. This book was released on 2013-12-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Arithmetic of Elliptic Curves

2013-03-09 Mathematics
Download The Arithmetic of Elliptic Curves PDF Online Free

Author :
Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 205/5 ( reviews)

GET EBOOK


Book Synopsis The Arithmetic of Elliptic Curves by : Joseph H. Silverman

Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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 approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Rational Points on Elliptic Curves

2013-04-17 Mathematics
Download Rational Points on Elliptic Curves PDF Online Free

Author :
Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 525/5 ( reviews)

GET EBOOK


Book Synopsis Rational Points on Elliptic Curves by : Joseph H. Silverman

Download or read book Rational Points on Elliptic Curves written by Joseph H. Silverman. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: 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 theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.

The Arithmetic of Elliptic Curves

2009-04-20 Mathematics
Download The Arithmetic of Elliptic Curves PDF Online Free

Author :
Release : 2009-04-20
Genre : Mathematics
Kind : eBook
Book Rating : 946/5 ( reviews)

GET EBOOK


Book Synopsis The Arithmetic of Elliptic Curves by : Joseph H. Silverman

Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman. This book was released on 2009-04-20. Available in PDF, EPUB and Kindle. Book excerpt: 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 approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Elliptic Curves and Arithmetic Invariants

2013-06-13 Mathematics
Download Elliptic Curves and Arithmetic Invariants PDF Online Free

Author :
Release : 2013-06-13
Genre : Mathematics
Kind : eBook
Book Rating : 571/5 ( reviews)

GET EBOOK


Book Synopsis Elliptic Curves and Arithmetic Invariants by : Haruzo Hida

Download or read book Elliptic Curves and Arithmetic Invariants written by Haruzo Hida. This book was released on 2013-06-13. Available in PDF, EPUB and Kindle. Book excerpt: 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-invariant, and similar topics. This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties. Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader. Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory. Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.

You may also like...