Advanced Topics In The Arithmetic Of Elliptic Curves
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Advanced Topics In The Arithmetic Of Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Advanced Topics In The Arithmetic Of Elliptic Curves written by Joseph H. Silverman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
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
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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-20
The Arithmetic Of Elliptic Curves written by Joseph H. Silverman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Mathematics categories.
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.
Arithmetic Algebraic Geometry
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Author : Brian Conrad
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2001
Arithmetic Algebraic Geometry written by Brian Conrad and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Arithmetical algebraic geometry categories.
The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the programme was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book should be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.
Advances On Superelliptic Curves And Their Applications
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Author : L. Beshaj
language : en
Publisher: IOS Press
Release Date : 2015-07-16
Advances On Superelliptic Curves And Their Applications written by L. Beshaj and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-16 with Computers categories.
This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.
Elliptic Curves And Arithmetic Invariants
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Author : Haruzo Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-13
Elliptic Curves And Arithmetic Invariants written by Haruzo Hida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-13 with Mathematics categories.
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.
Advances In Cryptology Asiacrypt 98
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Author : Kazuo Ohta
language : en
Publisher: Springer
Release Date : 2003-06-29
Advances In Cryptology Asiacrypt 98 written by Kazuo Ohta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-29 with Computers categories.
ASIACRYPT’98, the international conference covering all aspects of theory and application of cryptology and information security, is being held at Beijing Friendship Hotel from October 18 to 22. This is the fourth of the Asiacrypt conferences. ASIACRYPT’98 is sponsored by the State Key Laboratory of Information Security (SKLOIS), University of Science and Technology of China (USTC), and the Asiacrypt Steering Committee (ASC), in cooperation with the International Association for Cryptology Research (IACR). The 16-member Program Committee organized the scientific program and considered 118 submissions. Of these, 32 were accepted for presentation. The authors’ affiliations of the 118 submissions and the 32 accepted papers range over 18 and 13 countries or regions, respectively. The submitted version of each paper was sent to all members of the Program Committee and was extensively examined by at least three committee members and/or outside experts. The review process was rigorously blinded and the anonymity of each submission are maintained until the selection was completed. We followed the traditional policy that each member of the Program Committee could be an author of at most one accepted paper. These proceedings contain the revised versions of the 32 contributed talks as well as a short note written by one invited speaker. Comments from the Program Committee were taken into account in the revisions. However, the authors (not the committee) bear full responsibility for the contents of their papers.
Twisted L Functions And Monodromy Am 150 Volume 150
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
Twisted L Functions And Monodromy Am 150 Volume 150 written by Nicholas M. Katz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Mathematics categories.
For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.
Advances In Cryptology Asiacrypt 2019
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Author : Steven D. Galbraith
language : en
Publisher: Springer Nature
Release Date : 2019-11-22
Advances In Cryptology Asiacrypt 2019 written by Steven D. Galbraith and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-22 with Computers categories.
The three-volume set of LNCS 11921,11922, and 11923 constitutes the refereed proceedings of the 25th International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2019, held in Kobe, Japan, in December 2019. The 71 revised full papers presented were carefully reviewed and selected from 307 submissions. They are organized in topical sections on Lattices; Symmetric Cryptography; Isogenies; Obfuscation; Multiparty Computation; Quantum; E-cash and Blockchain; Codes; Authenticated Encryption; Multilinear Maps; Homomorphic Encryption; Combinatorial Cryptography; Signatures; Public Key Encryption; Side Channels; Functional Encryption; Zero Knowledge.
Advances In Cryptology Asiacrypt 2018
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Author : Thomas Peyrin
language : en
Publisher: Springer
Release Date : 2018-11-22
Advances In Cryptology Asiacrypt 2018 written by Thomas Peyrin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-22 with Computers categories.
The three-volume set of LNCS 11272, 11273, and 11274 constitutes the refereed proceedings of the 24th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2018, held in Brisbane, Australia, in December 2018. The 65 revised full papers were carefully selected from 234 submissions. They are organized in topical sections on Post-Quantum Cryptanalysis; Encrypted Storage; Symmetric-Key Constructions; Lattice Cryptography; Quantum Symmetric Cryptanalysis; Zero-Knowledge; Public Key and Identity-Based Encryption; Side-Channels; Signatures; Leakage-Resilient Cryptography; Functional/Inner Product/Predicate Encryption; Multi-party Computation; ORQM; Real World Protocols; Secret Sharing; Isogeny Cryptography; and Foundations.
Rational Points On Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer
Release Date : 2015-06-02
Rational Points On Elliptic Curves written by Joseph H. Silverman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-02 with Mathematics categories.
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.