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Author : Chong Hai Lim
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.:/5 (33 download)
Download or read book Endomorphism Rings of Jacobian Varietries of Fermat Curves written by Chong Hai Lim and published by . This book was released on 1990 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gary Cornell
Publisher : Springer Science & Business Media
ISBN 13 : 9780387946092
Total Pages : 608 pages
Book Rating : 4.9/5 (46 download)
Download or read book Modular Forms and Fermat’s Last Theorem written by Gary Cornell and published by Springer Science & Business Media. This book was released on 1997 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held at Boston University. The purpose of the conference, and indeed this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof, and to explain how his result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications.
Author : Samuele Anni
Publisher : American Mathematical Society
ISBN 13 : 1470467941
Total Pages : 198 pages
Book Rating : 4.4/5 (74 download)
Download or read book Arithmetic, Geometry, Cryptography, and Coding Theory 2021 written by Samuele Anni and published by American Mathematical Society. This book was released on 2022-07-06 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, held (online) from May 31 to June 4, 2021. For over thirty years, the biennial international conference AGC$^2$T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers together to forge connections between arithmetic geometry and its applications to coding theory and to cryptography. The papers illustrate the fruitful interaction between abstract theory and explicit computations, covering a large range of topics, including Belyi maps, Galois representations attached to elliptic curves, reconstruction of curves from their Jacobians, isogeny graphs of abelian varieties, hypergeometric equations, and Drinfeld modules.
Author : John Coates
Publisher : International Press of Boston
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.3/5 (91 download)
Download or read book Elliptic Curves, Modular Forms & Fermat's Last Theorem written by John Coates and published by International Press of Boston. This book was released on 1997 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings are based on a conference at the Chinese University of Hong Kong, held in response to Andrew Wile's conjecture that every elliptic curve over Q is modular. The survey article describing Wile's work is included as the first article in the present edition.
Author : Henri Darmon
Publisher : American Mathematical Soc.
ISBN 13 : 0821828681
Total Pages : 146 pages
Book Rating : 4.8/5 (218 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 2004 with total page 146 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 : Marc Hindry
Publisher : Springer Science & Business Media
ISBN 13 : 1461212103
Total Pages : 574 pages
Book Rating : 4.4/5 (612 download)
Download or read book Diophantine Geometry written by Marc Hindry and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Author :
Publisher :
ISBN 13 :
Total Pages : 1770 pages
Book Rating : 4.X/5 (6 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1770 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bjorn Poonen
Publisher : American Mathematical Soc.
ISBN 13 : 1470437732
Total Pages : 358 pages
Book Rating : 4.4/5 (74 download)
Download or read book Rational Points on Varieties written by Bjorn Poonen and published by American Mathematical Soc.. This book was released on 2017-12-13 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
Author :
Publisher :
ISBN 13 :
Total Pages : 606 pages
Book Rating : 4.3/5 (91 download)
Download or read book Russian Mathematical Surveys written by and published by . This book was released on 1972 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lubjana Beshaj
Publisher : American Mathematical Soc.
ISBN 13 : 1470442477
Total Pages : 358 pages
Book Rating : 4.4/5 (74 download)
Download or read book Algebraic Curves and Their Applications written by Lubjana Beshaj and published by American Mathematical Soc.. This book was released on 2019-02-26 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.
Author : Teo Mora
Publisher : Springer Science & Business Media
ISBN 13 : 9780817635466
Total Pages : 524 pages
Book Rating : 4.6/5 (354 download)
Download or read book Effective Methods in Algebraic Geometry written by Teo Mora and published by Springer Science & Business Media. This book was released on 1991 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: The symposium "MEGA-90 - Effective Methods in Algebraic Geome try" was held in Castiglioncello (Livorno, Italy) in April 17-211990. The themes - we quote from the "Call for papers" - were the fol lowing: - Effective methods and complexity issues in commutative algebra, pro jective geometry, real geometry, algebraic number theory - Algebraic geometric methods in algebraic computing Contributions in related fields (computational aspects of group theory, differential algebra and geometry, algebraic and differential topology, etc.) were also welcome. The origin and the motivation of such a meeting, that is supposed to be the first of a series, deserves to be explained. The subject - the theory and the practice of computation in alge braic geometry and related domains from the mathematical viewpoin- has been one of the themes of the symposia organized by SIGSAM (the Special Interest Group for Symbolic and Algebraic Manipulation of the Association for Computing Machinery), SAME (Symbolic and Algebraic Manipulation in Europe), and AAECC (the semantics of the name is vary ing; an average meaning is "Applied Algebra and Error Correcting Codes").
Author :
Publisher :
ISBN 13 :
Total Pages : 584 pages
Book Rating : 4.:/5 (35 download)
Download or read book Osaka Journal of Mathematics written by and published by . This book was released on 1972 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. W. S. Cassels
Publisher : Cambridge University Press
ISBN 13 : 9780521483704
Total Pages : 238 pages
Book Rating : 4.4/5 (837 download)
Download or read book Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 written by J. W. S. Cassels and published by Cambridge University Press. This book was released on 1996-04-18 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique insight into the topic of curves of genus 2, by two of the world's leading practitioners.
Author : Igor V. Dolgachev
Publisher : Cambridge University Press
ISBN 13 : 1139560786
Total Pages : 653 pages
Book Rating : 4.1/5 (395 download)
Download or read book Classical Algebraic Geometry written by Igor V. Dolgachev and published by Cambridge University Press. This book was released on 2012-08-16 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.
Author : Arjen K. Lenstra
Publisher : Springer
ISBN 13 : 3540478922
Total Pages : 138 pages
Book Rating : 4.5/5 (44 download)
Download or read book The Development of the Number Field Sieve written by Arjen K. Lenstra and published by Springer. This book was released on 2006-11-15 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.
Author :
Publisher :
ISBN 13 :
Total Pages : 468 pages
Book Rating : 4.:/5 (35 download)
Download or read book Symposia Mathematica written by and published by . This book was released on 1973 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paulos Tzermias
Publisher :
ISBN 13 :
Total Pages : 78 pages
Book Rating : 4.:/5 (33 download)
Download or read book Torsion in Mordell-Weil Groups of Fermat Jacobians written by Paulos Tzermias and published by . This book was released on 1995 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
