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Author : David Frederick Helm
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.:/5 (34 download)
Download or read book Jacobians of Shimura Curves and Jacquet-Langlands Correspondences written by David Frederick Helm and published by . This book was released on 2003 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Proceedings of the National Academy of Sciences
Publisher : National Academies Press
ISBN 13 : 9780309058759
Total Pages : 52 pages
Book Rating : 4.0/5 (587 download)
Download or read book Elliptic Curves and Modular Forms written by Proceedings of the National Academy of Sciences and published by National Academies Press. This book was released on 1998-01-01 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Emmanuel Peyre
Publisher : Springer Nature
ISBN 13 : 3030575594
Total Pages : 469 pages
Book Rating : 4.0/5 (35 download)
Download or read book Arakelov Geometry and Diophantine Applications written by Emmanuel Peyre and published by Springer Nature. This book was released on 2021-03-10 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.
Author : Brian David Conrad
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886915
Total Pages : 588 pages
Book Rating : 4.8/5 (869 download)
Download or read book Arithmetic Algebraic Geometry written by Brian David Conrad and published by American Mathematical Soc.. This book was released on with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular 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 would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.
Author : Moʻatsah ha-leʼumit le-meḥḳar ule-fituaḥ (Israel)
Publisher :
ISBN 13 :
Total Pages : 850 pages
Book Rating : 4.:/5 (327 download)
Download or read book Israel Journal of Mathematics written by Moʻatsah ha-leʼumit le-meḥḳar ule-fituaḥ (Israel) and published by . This book was released on 2007 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 826 pages
Book Rating : 4.E/5 ( download)
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2004 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vijaya Kumar Murty
Publisher : American Mathematical Soc.
ISBN 13 : 0821803131
Total Pages : 278 pages
Book Rating : 4.8/5 (218 download)
Download or read book Seminar on Fermat's Last Theorem written by Vijaya Kumar Murty and published by American Mathematical Soc.. This book was released on 1995 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most significant recent development in number theory is the work of Andrew Wiles on modular elliptic curves. Besides implying Fermat's Last Theorem, his work establishes a new reciprocity law. Reciprocity laws lie at the heart of number theory. Wiles' work draws on many of the tools of modern number theory and the purpose of this volume is to introduce readers to some of this background material. Based on a seminar held during 1993-1994 at the Fields Institute for Research in Mathematical Sciences, this book contains articles on elliptic curves, modular forms and modular curves, Serre's conjectures, Ribet's theorem, deformations of Galois representations, Euler systems, and annihilators of Selmer groups. All of the authors are well known in their field and have made significant contributions to the general area of elliptic curves, Galois representations, and modular forms. Features: Brings together a unique collection of number theoretic tools. Makes accessible the tools needed to understand one of the biggest breakthroughs in mathematics. Provides numerous references for further study.
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 :
Publisher :
ISBN 13 :
Total Pages : 1098 pages
Book Rating : 4.3/5 (91 download)
Download or read book Reviews in Number Theory 1984-96 written by and published by . This book was released on 1997 with total page 1098 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : M Van Der Put
Publisher : World Scientific
ISBN 13 : 9814546402
Total Pages : 378 pages
Book Rating : 4.8/5 (145 download)
Download or read book Drinfeld Modules, Modular Schemes And Applications written by M Van Der Put and published by World Scientific. This book was released on 1997-08-27 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his 1974 seminal paper 'Elliptic modules', V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as 'Drinfeld Modules'. They have many beautiful analogies with elliptic curves and abelian varieties. They study of their moduli spaces leads amongst others to explicit class field theory, Jacquet-Langlands theory, and a proof of the Shimura-Taniyama-Weil conjecture for global function fields.This book constitutes a carefully written instructional course of 12 lectures on these subjects, including many recent novel insights and examples. The instructional part is complemented by research papers centering around class field theory, modular forms and Heegner points in the theory of global function fields.The book will be indispensable for everyone who wants a clear view of Drinfeld's original work, and wants to be informed about the present state of research in the theory of arithmetic geometry over function fields.
Author :
Publisher :
ISBN 13 :
Total Pages : 720 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 1998 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Goss
Publisher : Walter de Gruyter
ISBN 13 : 3110886154
Total Pages : 493 pages
Book Rating : 4.1/5 (18 download)
Download or read book The Arithmetic of Function Fields written by David Goss and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Author : Dinesh S. Thakur
Publisher : World Scientific
ISBN 13 : 9812562389
Total Pages : 405 pages
Book Rating : 4.8/5 (125 download)
Download or read book Function Field Arithmetic written by Dinesh S. Thakur and published by World Scientific. This book was released on 2004 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an exposition of function field arithmetic withemphasis on recent developments concerning Drinfeld modules, thearithmetic of special values of transcendental functions (such as zetaand gamma functions and their interpolations), diophantineapproximation and related interesting open problems.
Author : Gerd Faltings
Publisher : Princeton University Press
ISBN 13 : 1400882478
Total Pages : 118 pages
Book Rating : 4.4/5 (8 download)
Download or read book Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 written by Gerd Faltings and published by Princeton University Press. This book was released on 2016-03-02 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
Author : Alexander Reznikov
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641153
Total Pages : 352 pages
Book Rating : 4.6/5 (411 download)
Download or read book Regulators in Analysis, Geometry and Number Theory written by Alexander Reznikov and published by Springer Science & Business Media. This book was released on 2000 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This work is an outgrowth of a conference held at the Hebrew University in Jerusalem on Regulators in Analysis, Geometry and Number Theory, and should appeal to a broad audience of graduate students and research mathematicians."--BOOK JACKET.
Author : Haruzo Hida
Publisher : Oxford University Press
ISBN 13 : 019857102X
Total Pages : 417 pages
Book Rating : 4.1/5 (985 download)
Download or read book Hilbert Modular Forms and Iwasawa Theory written by Haruzo Hida and published by Oxford University Press. This book was released on 2006-06-15 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describing the applications found for the Wiles and Taylor technique, this book generalizes the deformation theoretic techniques of Wiles-Taylor to Hilbert modular forms (following Fujiwara's treatment), and also discusses applications found by the author.
