# Advanced Topics in the Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) download epub

#### by **Joseph H. Silverman**

**Epub Book:**1411 kb. |

**Fb2 Book:**1546 kb.

This book is a continuation of the authors earlier book on elliptic curves, which was also an excellent book, and treats the more specialized topics in elliptic curves.

This book is a continuation of the authors earlier book on elliptic curves, which was also an excellent book, and treats the more specialized topics in elliptic curves. I cannot think of a branch of physics or engineering that has not made use of some facet of the theory of elliptic curves, and they have myriads of applications in other fields also, such as cryptography and financial engineering.

Find sources: "Graduate Texts in Mathematics" – news · newspapers · books .

Find sources: "Graduate Texts in Mathematics" – news · newspapers · books · scholar · JSTOR (November 2019) (Learn how and when to remove this template message). Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series tend to be written at a more advanced level than the similar Undergraduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level. Advanced Topics in the Arithmetic of Elliptic Curves, Joseph H. Silverman (1994

Graduate Texts in Mathematics Graduate Texts Mathematics Silverman,J. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems.

Graduate Texts in Mathematics Graduate Texts Mathematics Silverman,J. 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.

This book continues the study of elliptic curves by presenting six important, but somewhat more specialized topics: I. Elliptic and modular functions for the full modular group. II. IV. Néron models, Kodaira-N ron classification of special fibres, Tate's algorithm, and Ogg's nt formula. V. Tate's theory of q-curves over p-adic fields. VI. Néron's theory of canonical local height functions.

This is a graduate book on the theory of elliptic curves with an algebraic geometry approach to varieties. The book deals with the advanced topics of elliptic curves and the cohomological aspect of rational points on finite fields

This is a graduate book on the theory of elliptic curves with an algebraic geometry approach to varieties. The book deals with the advanced topics of elliptic curves and the cohomological aspect of rational points on finite fields. Difficult to read if one does not have the basic knowledge of the theory of elliptic curves. Dec 30, 2016 Will rated it it was amazing. A little less focused than the prequel, and a more difficult read, but the ending on "Tate curves" came at a complete surprise.

by Joseph H. Silverman. Graduate Texts in Mathematics (Book 151).

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. by Joseph H.

This is a superbly written introduction to elliptic curves. I dread the stiff elaborations, one finds in some german books with awkward idioms et. .I found it fascinating, how the elements of general theory, explicit formulae and geometric ideas (the group law on an elliptic curve is constructed via means of geometry) are interwoven. However, if you want to get a glimpse of such fundamental theorems like the Mordell-Weil theorem, you will need a solid understanding of the basics of algebraic number theory

Graduate Texts in Mathematics. The following material is covered in this book: I.

Graduate Texts in Mathematics. By (author) Joseph H.

Автор: Silverman Joseph H. Название: Arithmetic of Elliptic Curves ISBN: 1441918582 ISBN-13(EAN) .

Описание: The theory of elliptic curves is distinguished by the diversity of the methods used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry

*The Arithmetic of Elliptic Curves*, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational points and Siegel's theorem on the finiteness of the set of integral points. This book continues the study of elliptic curves by presenting six important, but somewhat more specialized topics: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Néron models, Kodaira-N ron classification of special fibres, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Néron's theory of canonical local height functions.

**Author:**Joseph H. Silverman

**ISBN:**0387943250

**Category:**Science & Math

**Subcategory:**Mathematics

**Language:**English

**Publisher:**Springer; 1 edition (November 4, 1994)

**Pages:**525 pages