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Author : Michael Laska
Publisher : Springer-Verlag
ISBN 13 : 3322875997
Total Pages : 220 pages
Book Rating : 4.3/5 (228 download)
Download or read book Elliptic Curves over Number Fields with Prescribed Reduction Type written by Michael Laska and published by Springer-Verlag. This book was released on 2013-03-09 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Susanne Schmitt
Publisher : Walter de Gruyter
ISBN 13 : 3110198010
Total Pages : 378 pages
Book Rating : 4.1/5 (11 download)
Download or read book Elliptic Curves written by Susanne Schmitt and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basics of the theory of elliptic curves should be known to everybody, be he (or she) a mathematician or a computer scientist. Especially everybody concerned with cryptography should know the elements of this theory. The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available.
Author : Siegfried Bosch
Publisher : Springer Science & Business Media
ISBN 13 : 3642514383
Total Pages : 336 pages
Book Rating : 4.6/5 (425 download)
Download or read book Néron Models written by Siegfried Bosch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Néron models were invented by A. Néron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of Néron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Néron models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of Néron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Néron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between Néron models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor.
Author : Matthew E. DeLong
Publisher :
ISBN 13 :
Total Pages : 150 pages
Book Rating : 4.3/5 (91 download)
Download or read book Relating Elliptic Curves to Three-ranks of Quadratic Number Fields written by Matthew E. DeLong and published by . This book was released on 1998 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dale Husemoller
Publisher : Springer Science & Business Media
ISBN 13 : 1475751192
Total Pages : 363 pages
Book Rating : 4.4/5 (757 download)
Download or read book Elliptic Curves written by Dale Husemoller and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 0387094946
Total Pages : 513 pages
Book Rating : 4.3/5 (87 download)
Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2009-04-20 with total page 513 pages. 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.
Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 9783540615811
Total Pages : 422 pages
Book Rating : 4.6/5 (158 download)
Download or read book Algorithmic Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 1996-08-07 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996. The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice theory, and coding.
Author : Andre Weil
Publisher : Springer Science & Business Media
ISBN 13 : 3662059789
Total Pages : 332 pages
Book Rating : 4.6/5 (62 download)
Download or read book Basic Number Theory. written by Andre Weil and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Itpzf}JlOV, li~oxov uoq>ZUJlCJ. 7:WV Al(JX., llpoj1. AE(Jj1. The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set ofnotes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by ChevaIley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very welt It contained abrief but essentially com plete account of the main features of c1assfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I inc1uded such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather c10sely at some critical points.
Author : Henri Darmon
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889459
Total Pages : 148 pages
Book Rating : 4.8/5 (894 download)
Download or read book Rational Points on Modular Elliptic Curves written by Henri Darmon and published by American Mathematical Soc.. This book was released on with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
Author : Joseph H. Silverman
Publisher : Springer
ISBN 13 : 0387962034
Total Pages : 400 pages
Book Rating : 4.3/5 (879 download)
Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer. This book was released on 1986 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the arithmetic theory of elliptic curves in its modern formulation through the use of basic algebraic number theory and algebraic geometry. It outlines necessary algebro-geometric results then proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. It also covers integral and rational points.
Author : Lawrence C. Washington
Publisher : CRC Press
ISBN 13 : 1420071475
Total Pages : 533 pages
Book Rating : 4.4/5 (2 download)
Download or read book Elliptic Curves written by Lawrence C. Washington and published by CRC Press. This book was released on 2008-04-03 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application
Author : Peter F. Stiller
Publisher : Springer Science & Business Media
ISBN 13 : 3322907082
Total Pages : 201 pages
Book Rating : 4.3/5 (229 download)
Download or read book Automorphic Forms and the Picard Number of an Elliptic Surface written by Peter F. Stiller and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: In studying an algebraic surface E, which we assume is non-singular and projective over the field of complex numbers t, it is natural to study the curves on this surface. In order to do this one introduces various equivalence relations on the group of divisors (cycles of codimension one). One such relation is algebraic equivalence and we denote by NS(E) the group of divisors modulo algebraic equivalence which is called the N~ron-Severi group of the surface E. This is known to be a finitely generated abelian group which can be regarded naturally as a subgroup of 2 H (E,Z). The rank of NS(E) will be denoted p and is known as the Picard number of E. 2 Every divisor determines a cohomology class in H(E,E) which is of I type (1,1), that is to say a class in H(E,9!) which can be viewed as a 2 subspace of H(E,E) via the Hodge decomposition. The Hodge Conjecture asserts in general that every rational cohomology class of type (p,p) is algebraic. In our case this is the Lefschetz Theorem on (I,l)-classes: Every cohomology class 2 2 is the class associated to some divisor. Here we are writing H (E,Z) for 2 its image under the natural mapping into H (E,t). Thus NS(E) modulo 2 torsion is Hl(E,n!) n H(E,Z) and th 1 b i f h -~ p measures e a ge ra c part 0 t e cohomology.
Author : Wilhelm Stoll
Publisher : Springer Science & Business Media
ISBN 13 : 3663052923
Total Pages : 358 pages
Book Rating : 4.6/5 (63 download)
Download or read book Value Distribution Theory for Meromorphic Maps written by Wilhelm Stoll and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Value distribution theory studies the behavior of mermorphic maps. Let f: M - N be a merom orphic map between complex manifolds. A target family CI ~ (Ea1aEA of analytic subsets Ea of N is given where A is a connected. compact complex manifold. The behavior of the inverse 1 family ["'(CI) = (f- {E )laEA is investigated. A substantial theory has been a created by many contributors. Usually the targets Ea stay fixed. However we can consider a finite set IJ of meromorphic maps g : M - A and study the incidence f{z) E Eg(z) for z E M and some g E IJ. Here we investigate this situation: M is a parabolic manifold of dimension m and N = lP n is the n-dimensional projective space. The family of hyperplanes in lP n is the target family parameterized by the dual projective space lP* We obtain a Nevanlinna theory consisting of several n First Main Theorems. Second Main Theorems and Defect Relations and extend recent work by B. Shiffman and by S. Mori. We use the Ahlfors-Weyl theory modified by the curvature method of Cowen and Griffiths. The Introduction consists of two parts. In Part A. we sketch the theory for fixed targets to provide background for those who are familar with complex analysis but are not acquainted with value distribution theory.
Author : Gilbert Hector
Publisher : Springer Science & Business Media
ISBN 13 : 3322901157
Total Pages : 247 pages
Book Rating : 4.3/5 (229 download)
Download or read book Introduction to the Geometry of Foliations, Part A written by Gilbert Hector and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foliation theory grew out of the theory of dynamical systems on manifolds and Ch. Ehresmann's connection theory on fibre bundles. Pioneer work was done between 1880 and 1940 by H. Poincare, I. Bendixson, H. Kneser, H. Whitney, and IV. Kaplan - to name a few - who all studied "regular curve families" on surfaces, and later by Ch. Ehresmann, G. Reeb, A. Haefliger and otners between 1940 and 1960. Since then the subject has developed from a collection of a few papers to a wide field of research. ~owadays, one usually distinguishes between two main branches of foliation theory, the so-called quantitative theory (including homotopy theory and cnaracteristic classes) on the one hand, and the qualitative or geometrie theory on the other. The present volume is the first part of a monograph on geometrie aspects of foliations. Our intention here is to present some fundamental concepts and results as weIl as a great number of ideas and examples of various types. The selection of material from only one branch of the theory is conditioned not only by the authors' personal interest but also by the wish to give a systematic and detailed treatment, including complete proofs of all main results. We hope that tilis goal has been achieved
Author : Gerd Faltings
Publisher : Springer Science & Business Media
ISBN 13 : 3663068129
Total Pages : 276 pages
Book Rating : 4.6/5 (63 download)
Download or read book Rational Points written by Gerd Faltings and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alan Howard
Publisher : Springer Science & Business Media
ISBN 13 : 3663068161
Total Pages : 357 pages
Book Rating : 4.6/5 (63 download)
Download or read book Contributions to Several Complex Variables written by Alan Howard and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1960 Wilhelm Stoll joined the University of Notre Dame faculty as Professor of Mathematics, and in October, 1984 the university acknowledged his many years of distinguished service by holding a conference in complex analysis in his honour. This volume is the proceedings of that conference. It was our priviledge to serve, along with Nancy K. Stanton, as conference organizers. We are grateful to the College of Science of the University of Notre Dame and to the National Science Foundation for their support. In the course of a career that has included the publication of over sixty research articles and the supervision of eighteen doctoral students, Wilhelm Stoll has won the affection and respect of his colleagues for his diligence, integrity and humaneness. The influence of his ideas and insights and the subsequent investigations they have inspired is attested to by several of the articles in the volume. On behalf of the conference partipants and contributors to this volume, we wish Wilhelm Stoll many more years of happy and devoted service to mathematics. Alan Howard Pit-Mann Wong VII III ~ c: ... ~ c: o U CI> .r. ~ .... o e ::J ~ o a:: a. ::J o ... (.!:J VIII '" Q) g> a. '" Q) E z '" ..... o Q) E Q) ..c eX IX Participants on the Group Picture Qi-keng LU, Professor, Chinese Academy of Science, Peking, China.
Author : Lawrence C. Washington
Publisher : CRC Press
ISBN 13 : 9780203484029
Total Pages : 446 pages
Book Rating : 4.4/5 (84 download)
Download or read book Elliptic Curves written by Lawrence C. Washington and published by CRC Press. This book was released on 2003-05-28 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to
