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Author | : John William Scott Cassels |
Publisher | : Cambridge University Press |
Total Pages | : 148 |
Release | : 1991-11-21 |
Genre | : Mathematics |
ISBN | : 9780521425308 |
Download LMSST: 24 Lectures on Elliptic Curves Book in PDF, ePub and Kindle
A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.
Author | : J. W. S. Cassels |
Publisher | : |
Total Pages | : 146 |
Release | : 1991 |
Genre | : Curves, Elliptic |
ISBN | : 9781107094505 |
Download LMSST Book in PDF, ePub and Kindle
A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.
Author | : Joseph H. Silverman |
Publisher | : Springer Science & Business Media |
Total Pages | : 292 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475742525 |
Download Rational Points on Elliptic Curves Book in PDF, ePub and Kindle
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.
Author | : J. W. S. Cassels |
Publisher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 1991-11-21 |
Genre | : Mathematics |
ISBN | : 9780521425308 |
Download LMSST: 24 Lectures on Elliptic Curves Book in PDF, ePub and Kindle
The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.
Author | : A. Robert |
Publisher | : Springer |
Total Pages | : 272 |
Release | : 2009-02-27 |
Genre | : Mathematics |
ISBN | : 3540469168 |
Download Elliptic Curves Book in PDF, ePub and Kindle
Author | : John William Scott Cassels |
Publisher | : |
Total Pages | : 146 |
Release | : 2014-05-14 |
Genre | : MATHEMATICS |
ISBN | : 9781107088290 |
Download Lmsst: 24 Lectures on Elliptic Curves Book in PDF, ePub and Kindle
A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.
Author | : Spencer J. Bloch |
Publisher | : American Mathematical Soc. |
Total Pages | : 114 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821829734 |
Download Higher Regulators, Algebraic $K$-Theory, and Zeta Functions of Elliptic Curves Book in PDF, ePub and Kindle
This is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more).
Author | : Jean-P. Serre |
Publisher | : Springer Science & Business Media |
Total Pages | : 228 |
Release | : 2013-06-29 |
Genre | : Technology & Engineering |
ISBN | : 3663106322 |
Download Lectures on the Mordell-Weil Theorem Book in PDF, ePub and Kindle
The book is based on a course given by J.-P. Serre at the Collège de France in 1980 and 1981. Basic techniques in Diophantine geometry are covered, such as heights, the Mordell-Weil theorem, Siegel's and Baker's theorems, Hilbert's irreducibility theorem, and the large sieve. Included are applications to, for example, Mordell's conjecture, the construction of Galois extensions, and the classical class number 1 problem. Comprehensive bibliographical references.
Author | : Dale Husemoller |
Publisher | : Springer Science & Business Media |
Total Pages | : 363 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1475751192 |
Download Elliptic Curves Book in PDF, ePub and Kindle
The book divides naturally into several parts according to the level of the material, the background required of the reader, and the style of presentation with respect to details of proofs. For example, the first part, to Chapter 6, is undergraduate in level, the second part requires a background in Galois theory and the third some complex analysis, while the last parts, from Chapter 12 on, are mostly at graduate level. A general outline ofmuch ofthe material can be found in Tate's colloquium lectures reproduced as an article in Inven tiones [1974]. The first part grew out of Tate's 1961 Haverford Philips Lectures as an attempt to write something for publication c10sely related to the original Tate notes which were more or less taken from the tape recording of the lectures themselves. This inc1udes parts of the Introduction and the first six chapters The aim ofthis part is to prove, by elementary methods, the Mordell theorem on the finite generation of the rational points on elliptic curves defined over the rational numbers. In 1970 Tate teturned to Haverford to give again, in revised form, the originallectures of 1961 and to extend the material so that it would be suitable for publication. This led to a broader plan forthe book.
Author | : Joseph H. Silverman |
Publisher | : Springer Science & Business Media |
Total Pages | : 414 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475719205 |
Download The Arithmetic of Elliptic Curves Book in PDF, ePub and Kindle
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.