Analytic Theory Of Abelian Varieties
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Analytic Theory Of Abelian Varieties
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Author : H. P. F. Swinnerton-Dyer
language : en
Publisher: Cambridge University Press
Release Date : 1974-12-12
Analytic Theory Of Abelian Varieties written by H. P. F. Swinnerton-Dyer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-12-12 with Mathematics categories.
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
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Author : H. P. F. Swinnerton-Dyer
language : en
Publisher:
Release Date : 1974
Analytic Theory Of Abelian Varieties written by H. P. F. Swinnerton-Dyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Abelian varieties categories.
This introduction presupposes little more than a basic course in complex variables.
Abelian Varieties Theta Functions And The Fourier Transform
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Author : Alexander Polishchuk
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-21
Abelian Varieties Theta Functions And The Fourier Transform written by Alexander Polishchuk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-21 with Mathematics categories.
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Abelian Varieties
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Author : David Mumford
language : en
Publisher: Debolsillo
Release Date : 2008
Abelian Varieties written by David Mumford and has been published by Debolsillo this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Abelian varieties categories.
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.''
Analytic Theory Of Abelian Varieties
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Author : Sir Peter Swinnerton-Dyer
language : en
Publisher:
Release Date : 1974
Analytic Theory Of Abelian Varieties written by Sir Peter Swinnerton-Dyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Abelian varieties categories.
Complex Abelian Varieties
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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.
Degeneration Of Abelian Varieties
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Author : Gerd Faltings
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Degeneration Of Abelian Varieties written by Gerd Faltings 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 2013-04-17 with Mathematics categories.
The topic of this book is the theory of degenerations of abelian varieties and its application to the construction of compactifications of moduli spaces of abelian varieties. These compactifications have applications to diophantine problems and, of course, are also interesting in their own right. Degenerations of abelian varieties are given by maps G - S with S an irre ducible scheme and G a group variety whose generic fibre is an abelian variety. One would like to classify such objects, which, however, is a hopeless task in this generality. But for more specialized families we can obtain more: The most important theorem about degenerations is the stable reduction theorem, which gives some evidence that for questions of compactification it suffices to study semi-abelian families; that is, we may assume that G is smooth and flat over S, with fibres which are connected extensions of abelian varieties by tori. A further assumption will be that the base S is normal, which makes such semi-abelian families extremely well behaved. In these circumstances, we give a rather com plete classification in case S is the spectrum of a complete local ring, and for general S we can still say a good deal. For a complete base S = Spec(R) (R a complete and normal local domain) the main result about degenerations says roughly that G is (in some sense) a quotient of a covering G by a group of periods.
Complex Tori And Abelian Varieties
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Author : Olivier Debarre
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Complex Tori And Abelian Varieties written by Olivier Debarre 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 2005 with Mathematics categories.
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.
Rigid Analytic Geometry And Its Applications
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Author : Jean Fresnel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-06
Rigid Analytic Geometry And Its Applications written by Jean Fresnel 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 2003-11-06 with Mathematics categories.
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.
Moduli Of Abelian Varieties
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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.