Analytic Theory Of Abelian Varieties

Analytic Theory Of Abelian Varieties Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Analytic Theory Of Abelian Varieties book. This book definitely worth reading, it is an incredibly well-written.

Analytic Theory of Abelian Varieties

H. P. F. Swinnerton-Dyer
Analytic Theory of Abelian Varieties Book PDF

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 105 pages
File Size : 42,6 Mb
Release : 1974-12-12
Category : Mathematics
ISBN : 9780521205269

Get Book

Analytic Theory of Abelian Varieties by H. P. F. Swinnerton-Dyer Pdf

The study of abelian manifolds forms a natural generalization of the theory of elliptic functions, that is, of doubly periodic functions of one complex variable. When an abelian manifold is embedded in a projective space it is termed an abelian variety in an algebraic geometrical sense. This introduction presupposes little more than a basic course in complex variables. The notes contain all the material on abelian manifolds needed for application to geometry and number theory, although they do not contain an exposition of either application. Some geometrical results are included however.

Analytic Theory of Abelian Varieties

H. P. F. Swinnerton-Dyer
Analytic Theory of Abelian Varieties Book PDF

Author : H. P. F. Swinnerton-Dyer
Publisher : Unknown
Page : 0 pages
File Size : 43,6 Mb
Release : 1974
Category : Abelian varieties
ISBN : 1107093252

Get Book

Analytic Theory of Abelian Varieties by H. P. F. Swinnerton-Dyer Pdf

This introduction presupposes little more than a basic course in complex variables.

Introduction to Abelian Varieties

Vijaya Kumar Murty
Introduction to Abelian Varieties Book PDF

Author : Vijaya Kumar Murty
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 43,8 Mb
Release : 1993
Category : Abelian varieties
ISBN : 9780821811795

Get Book

Introduction to Abelian Varieties by Vijaya Kumar Murty Pdf

This book presents an elementary and self-contained approach to Abelian varieties, a subject that plays a central role in algebraic and analytic geometry, number theory, and complex analysis. The book is based on notes from a course given at Concordia University and would be useful for independent study or as a textbook for graduate courses in complex analysis, Riemann surfaces, number theory, or analytic geometry. Murty works mostly over the complex numbers, discussing the theorem of Abel-Jacobi and Lefschetz's theorem on projective embeddings. After presenting some examples, Murty touches on Abelian varieties over number fields, as well as the conjecture of Tate (Faltings's theorem) and its relation to Mordell's conjecture. References are provided to guide the reader in further study.

Abelian Varieties, Theta Functions and the Fourier Transform

Alexander Polishchuk
Abelian Varieties Theta Functions and the Fourier Transform Book PDF

Author : Alexander Polishchuk
Publisher : Cambridge University Press
Page : 308 pages
File Size : 43,6 Mb
Release : 2003-04-21
Category : Mathematics
ISBN : 9780521808040

Get Book

Abelian Varieties, Theta Functions and the Fourier Transform by Alexander Polishchuk Pdf

Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.

Complex Tori and Abelian Varieties

Olivier Debarre
Complex Tori and Abelian Varieties Book PDF

Author : Olivier Debarre
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 41,9 Mb
Release : 2005
Category : Mathematics
ISBN : 0821831658

Get Book

Complex Tori and Abelian Varieties by Olivier Debarre Pdf

This graduate-level textbook introduces the classical theory of complex tori and abelian varieties, while presenting in parallel more modern aspects of complex algebraic and analytic geometry. Beginning with complex elliptic curves, the book moves on to the higher-dimensional case, giving characterizations from different points of view of those complex tori which are abelian varieties, i.e., those that can be holomorphically embedded in a projective space. This allows, on the one hand, for illuminating the computations of nineteenth-century mathematicians, and on the other, familiarizing readers with more recent theories. Complex tori are ideal in this respect: One can perform "hands-on" computations without the theory being totally trivial. Standard theorems about abelian varieties are proved, and moduli spaces are discussed. Recent results on the geometry and topology of some subvarieties of a complex torus are also included. The book contains numerous examples and exercises. It is a very good starting point for studying algebraic geometry, suitable for graduate students and researchers interested in algebra and algebraic geometry. Information for our distributors: SMF members are entitled to AMS member discounts.

Abelian Varieties

David Mumford
Abelian Varieties Book PDF

Author : David Mumford
Publisher : Debolsillo
Page : 0 pages
File Size : 49,9 Mb
Release : 2008
Category : Abelian varieties
ISBN : 8185931860

Get Book

Abelian Varieties by David Mumford Pdf

This is a reprinting of the revised second edition (1974) of David Mumford's classic 1970 book. It gives a systematic account of the basic results about abelian varieties. It includes expositions of analytic methods applicable over the ground field of complex numbers, as well as of scheme-theoretic methods used to deal with inseparable isogenies when the ground field has positive characteristic. A self-contained proof of the existence of the dual abelian variety is given. The structure of the ring of endomorphisms of an abelian variety is discussed. These are appendices on Tate's theorem on endomorphisms of abelian varieties over finite fields (by C. P. Ramanujam) and on the Mordell-Weil theorem (by Yuri Manin). David Mumford was awarded the 2007 AMS Steele Prize for Mathematical Exposition. According to the citation: ``Abelian Varieties ... remains the definitive account of the subject ... the classical theory is beautifully intertwined with the modern theory, in a way which sharply illuminates both ... [It] will remain for the foreseeable future a classic to which the reader returns over and over.''

Complex Abelian Varieties

Herbert Lange,Christina Birkenhake
Complex Abelian Varieties Book PDF

Author : Herbert Lange,Christina Birkenhake
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 40,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662027882

Get Book

Complex Abelian Varieties by Herbert Lange,Christina Birkenhake Pdf

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.

Complex Abelian Varieties and Theta Functions

George R. Kempf
Complex Abelian Varieties and Theta Functions Book PDF

Author : George R. Kempf
Publisher : Springer Science & Business Media
Page : 108 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642760792

Get Book

Complex Abelian Varieties and Theta Functions by George R. Kempf Pdf

Abelian varieties are a natural generalization of elliptic curves to higher dimensions, whose geometry and classification are as rich in elegant results as in the one-dimensional ease. The use of theta functions, particularly since Mumford's work, has been an important tool in the study of abelian varieties and invertible sheaves on them. Also, abelian varieties play a significant role in the geometric approach to modern algebraic number theory. In this book, Kempf has focused on the analytic aspects of the geometry of abelian varieties, rather than taking the alternative algebraic or arithmetic points of view. His purpose is to provide an introduction to complex analytic geometry. Thus, he uses Hermitian geometry as much as possible. One distinguishing feature of Kempf's presentation is the systematic use of Mumford's theta group. This allows him to give precise results about the projective ideal of an abelian variety. In its detailed discussion of the cohomology of invertible sheaves, the book incorporates material previously found only in research articles. Also, several examples where abelian varieties arise in various branches of geometry are given as a conclusion of the book.

Abelian Varieties with Complex Multiplication and Modular Functions

Goro Shimura
Abelian Varieties with Complex Multiplication and Modular Functions Book PDF

Author : Goro Shimura
Publisher : Princeton University Press
Page : 232 pages
File Size : 46,9 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781400883943

Get Book

Abelian Varieties with Complex Multiplication and Modular Functions by Goro Shimura Pdf

Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively.

80 Years of Zentralblatt MATH

Olaf Teschke,Bernd Wegner,Dirk Werner
80 Years of Zentralblatt MATH Book PDF

Author : Olaf Teschke,Bernd Wegner,Dirk Werner
Publisher : Springer Science & Business Media
Page : 211 pages
File Size : 40,7 Mb
Release : 2011-08-27
Category : Mathematics
ISBN : 9783642211720

Get Book

80 Years of Zentralblatt MATH by Olaf Teschke,Bernd Wegner,Dirk Werner Pdf

Founded in 1931 by Otto Neugebauer as the printed documentation service “Zentralblatt für Mathematik und ihre Grenzgebiete”, Zentralblatt MATH (ZBMATH) celebrates its 80th anniversary in 2011. Today it is the most comprehensive and active reference database in pure and applied mathematics worldwide. Many prominent mathematicians have been involved in this service as reviewers or editors and have, like all mathematicians, left their footprints in ZBMATH, in a long list of entries describing all of their research publications in mathematics. This book provides one review from each of the 80 years of ZBMATH. Names like Courant, Kolmogorov, Hardy, Hirzebruch, Faltings and many others can be found here. In addition to the original reviews, the book offers the authors' profiles indicating their co-authors, their favorite journals and the time span of their publication activities. In addition to this, a generously illustrated essay by Silke Göbel describes the history of ZBMATH.

Analytic Number Theory

Henryk Iwaniec,Emmanuel Kowalski
Analytic Number Theory Book PDF

Author : Henryk Iwaniec,Emmanuel Kowalski
Publisher : American Mathematical Soc.
Page : 615 pages
File Size : 54,8 Mb
Release : 2021-10-14
Category : Education
ISBN : 9781470467708

Get Book

Analytic Number Theory by Henryk Iwaniec,Emmanuel Kowalski Pdf

Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.

Compactifying Moduli Spaces for Abelian Varieties

Martin C. Olsson
Compactifying Moduli Spaces for Abelian Varieties Book PDF

Author : Martin C. Olsson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 48,7 Mb
Release : 2008-08-25
Category : Mathematics
ISBN : 9783540705185

Get Book

Compactifying Moduli Spaces for Abelian Varieties by Martin C. Olsson Pdf

This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.

Degeneration of Abelian Varieties

Gerd Faltings,Ching-Li Chai
Degeneration of Abelian Varieties Book PDF

Author : Gerd Faltings,Ching-Li Chai
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 40,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662026328

Get Book

Degeneration of Abelian Varieties by Gerd Faltings,Ching-Li Chai Pdf

A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.

Introduction to Abelian Varieties

V. Kumar Murty
Introduction to Abelian Varieties Book PDF

Author : V. Kumar Murty
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 54,8 Mb
Release : 1986
Category : Abelian groups
ISBN : 082187005X

Get Book

Introduction to Abelian Varieties by V. Kumar Murty Pdf

This book presents an elementary and self-contained approach to Abelian varieties, a subject that plays a central role in algebraic and analytic geometry, number theory, and complex analysis. The book is based on notes from a course given at Concordia University and would be useful for independent study or as a textbook for graduate courses in complex analysis, Riemann surfaces, number theory, or analytic geometry. Murty works mostly over the complex numbers, discussing the theorem of Abel-Jacobi and Lefschetz's theorem on projective embeddings. After presenting some examples, Murty touches on Abelian varieties over number fields, as well as the conjecture of Tate (Faltings's theorem) and its relation to Mordell's conjecture. References are provided to guide the reader in further study.

Rigid Analytic Geometry and Its Applications

Jean Fresnel,Marius van der Put
Rigid Analytic Geometry and Its Applications Book PDF

Author : Jean Fresnel,Marius van der Put
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200413

Get Book

Rigid Analytic Geometry and Its Applications by Jean Fresnel,Marius van der Put Pdf

Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.