Modular Curves And Abelian Varieties

DOWNLOAD

Download Modular Curves And Abelian Varieties PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Modular Curves And Abelian Varieties book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Modular Curves And Abelian Varieties

DOWNLOAD
Author : John Cremona
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-23

Modular Curves And Abelian Varieties written by John Cremona 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 2004-02-23 with Mathematics categories.

This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matemàtica (Bellaterra, Barcelona). The articles in this volume present the latest achievements in this extremely active field and will be of interest both to specialists and to students and researchers. Many contributions focus on generalizations of the Shimura-Taniyama conjecture to varieties such as elliptic Q-curves and Abelian varieties of GL_2-type. The book also includes several key articles in the subject that do not correspond to conference lectures.

Modular Curves And Abelian Varieties

DOWNLOAD
Author : John Cremona
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Modular Curves And Abelian Varieties written by John Cremona and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matemtica (Bellaterra, Barcelona). The articles in this volume present the latest achievements in this extremely active field and will be of interest both to specialists and to students and researchers. Many contributions focus on generalizations of the Shimura-Taniyama conjecture to varieties such as elliptic Q-curves and Abelian varieties of GL_2-type. The book also includes several key articles in the subject that do not correspond to conference lectures.

Moduli Of Abelian Varieties

DOWNLOAD
Author : C. Faber
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-03

Moduli Of Abelian Varieties written by C. Faber 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 2001-03 with Mathematics categories.

Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics. Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field. The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics.

Modular Forms And Fermat S Last Theorem

DOWNLOAD
Author : Gary Cornell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Modular Forms And Fermat S Last Theorem written by Gary Cornell 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.

This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' 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, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem.

The Arithmetic Of Elliptic Curves

DOWNLOAD
Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

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 2013-03-09 with Mathematics categories.

The preface to a textbook frequently contains the author's justification for offering the public "another book" on the given subject. For our chosen topic, the arithmetic of elliptic curves, there is little need for such an apologia. Considering the vast amount of research currently being done in this area, the paucity of introductory texts is somewhat surprising. Parts of the theory are contained in various books of Lang (especially [La 3] and [La 5]); and there are books of Koblitz ([Kob]) and Robert ([Rob], now out of print) which concentrate mostly on the analytic and modular theory. In addition, survey articles have been written by Cassels ([Ca 7], really a short book) and Tate ([Ta 5J, which is beautifully written, but includes no proofs). Thus the author hopes that this volume will fill a real need, both for the serious student who wishes to learn the basic facts about the arithmetic of elliptic curves; and for the research mathematician who needs a reference source for those same basic facts. Our approach is more algebraic than that taken in, say, [La 3] or [La 5], where many of the basic theorems are derived using complex analytic methods and the Lefschetz principle. For this reason, we have had to rely somewhat more on techniques from algebraic geometry. However, the geom etry of (smooth) curves, which is essentially all that we use, does not require a great deal of machinery.

A First Course In Modular Forms

DOWNLOAD
Author : Fred Diamond
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-01-19

A First Course In Modular Forms written by Fred Diamond 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 2005-01-19 with Mathematics categories.

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.

Introduction To Modular Forms

DOWNLOAD
Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-01

Introduction To Modular Forms written by Serge Lang 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 2001-08-01 with Mathematics categories.

From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#

Modular Forms A Computational Approach

DOWNLOAD
Author : William A. Stein
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-02-13

Modular Forms A Computational Approach written by William A. Stein and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-13 with Mathematics categories.

This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.

Quaternion Algebras

DOWNLOAD
Author : John Voight
language : en
Publisher: Springer Nature
Release Date : 2021-06-28

Quaternion Algebras written by John Voight and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Mathematics categories.

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.

Complex Abelian Varieties

DOWNLOAD
Author : Herbert Lange
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Complex Abelian Varieties written by Herbert Lange 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 2013-03-09 with Mathematics categories.

Abelian varieties are special examples of projective varieties. As such theycan be described by a set of homogeneous polynomial equations. The theory ofabelian varieties originated in the beginning of the ninetheenth centrury with the work of Abel and Jacobi. The subject of this book is the theory of abelian varieties over the field of complex numbers, and it covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an abelian variety, their equations and geometric properties. Moreover several moduli spaces of abelian varieties with additional structure are constructed. Some special results onJacobians and Prym varieties allow applications to the theory of algebraic curves. The main tools for the proofs are the theta group of a line bundle, introduced by Mumford, and the characteristics, to be associated to any nondegenerate line bundle. They are a direct generalization of the classical notion of characteristics of theta functions.