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Rational Points On Curves Over Finite Fields
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Book Synopsis Rational Points on Curves Over Finite Fields by : Harald Niederreiter
Download or read book Rational Points on Curves Over Finite Fields written by Harald Niederreiter and published by Cambridge University Press. This book was released on 2001-06-14 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discussion of theory and applications of algebraic curves over finite fields with many rational points.
Book Synopsis Rational Points on Curves Over Finite Fields by : Jean-Pierre Serre
Download or read book Rational Points on Curves Over Finite Fields written by Jean-Pierre Serre and published by . This book was released on 2020 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1985 Jean-Pierre Serre gave a series of lectures at Harvard University on the number of points of curves over finite fields. Based on notes taken at that time by F. Q. Gouvea, the present revised and completed documents provides an insightful introduction to this beautiful topic and to most of the ideas that have been developed in this area during the last 30 years.
Book Synopsis Rational Points on Elliptic Curves by : Joseph H. Silverman
Download or read book Rational Points on Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Rational Points on Curves Over Finite Fields by : Søren Have Hansen
Download or read book Rational Points on Curves Over Finite Fields written by Søren Have Hansen and published by . This book was released on 1995 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Curves over a Finite Field by : J. W. P. Hirschfeld
Download or read book Algebraic Curves over a Finite Field written by J. W. P. Hirschfeld and published by Princeton University Press. This book was released on 2013-03-25 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
Download or read book Lecture Notes Series written by and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Number of Rational Points on Curves Over Finite Fields by : Jean-Pierre Serre
Download or read book The Number of Rational Points on Curves Over Finite Fields written by Jean-Pierre Serre and published by . This book was released on 1985 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rational Points on Curves Over Finite Fields by : Jean-Pierre Serre
Download or read book Rational Points on Curves Over Finite Fields written by Jean-Pierre Serre and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Geometry And Its Applications: Dedicated To Gilles Lachaud On His 60th Birthday - Proceedings Of The First Saga Conference by : Robert Rolland
Download or read book Algebraic Geometry And Its Applications: Dedicated To Gilles Lachaud On His 60th Birthday - Proceedings Of The First Saga Conference written by Robert Rolland and published by World Scientific. This book was released on 2008-04-17 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.
Book Synopsis Algebraic Curves Over Finite Fields by : Carlos Moreno
Download or read book Algebraic Curves Over Finite Fields written by Carlos Moreno and published by Cambridge University Press. This book was released on 1993-10-14 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.
Book Synopsis Rational Points on Varieties by : Bjorn Poonen
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.
Book Synopsis Rational Points on Modular Elliptic Curves by : Henri Darmon
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.
Book Synopsis Construction of Algebraic Curves with Many Rational Points Over Finite Fields by : Virgile Ducet
Download or read book Construction of Algebraic Curves with Many Rational Points Over Finite Fields written by Virgile Ducet and published by . This book was released on 2013 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the number of rational points of a curve defined over a finite field naturally falls into two cases: when the genus is small (typically g
Book Synopsis Rational Points on Elliptic Curves Over Finite Fields by : 黃柏嶧
Download or read book Rational Points on Elliptic Curves Over Finite Fields written by 黃柏嶧 and published by . This book was released on 1999 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Codes on Algebraic Curves by : Serguei A. Stepanov
Download or read book Codes on Algebraic Curves written by Serguei A. Stepanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.
Book Synopsis Applications of Curves over Finite Fields by : Michael D. Fried
Download or read book Applications of Curves over Finite Fields written by Michael D. Fried and published by American Mathematical Soc.. This book was released on 1999 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the results of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington (Seattle). The talks were devoted to various aspects of the theory of algebraic curves over finite fields and its numerous applications. The three basic themes are the following: 1. Curves with many rational points. Several articles describe main approaches to the construction of such curves: the Drinfeld modules and fiber product methods, the moduli space approach, and the constructions using classical curves. 2. Monodromy groups of characteristic $p$ covers. A number of authors presented the results and conjectures related to the study of the monodromy groups of curves over finite fields. In particular, they study the monodromy groups from genus 0 covers, reductions of covers, and explicit computation of monodromy groups over finite fields. 3. Zeta functions and trace formulas. To a large extent, papers devoted to this topic reflect the contributions of Professor Bernard Dwork and his students. This conference was the last attended by Professor Dwork before his death, and several papers inspired by his presence include commentaries about the applications of trace formulas and L-function. The volume also contains a detailed introduction paper by Professor Michael Fried, which helps the reader to navigate the material presented in the book.
Book Synopsis Lefschetz Theorems and Dependent Rational Points on Curves Over Finite Fields by : Johan P. Hansen
Download or read book Lefschetz Theorems and Dependent Rational Points on Curves Over Finite Fields written by Johan P. Hansen and published by . This book was released on 1999 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
