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Curves And Abelian Varieties
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Book Synopsis Modular Curves and Abelian Varieties by : John Cremona
Download or read book Modular Curves and Abelian Varieties written by John Cremona and published by Birkhäuser. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Curves and Abelian Varieties by : Valery Alexeev
Download or read book Curves and Abelian Varieties written by Valery Alexeev and published by American Mathematical Soc.. This book was released on 2008 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes." "In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors. of compactified Jucobiuns of singular curves, and of "strange duality" among moduli spaces of vector bundles on algebraic varieties."--BOOK JACKET.
Book Synopsis Introduction to Abelian Varieties by : Vijaya Kumar Murty
Download or read book Introduction to Abelian Varieties written by Vijaya Kumar Murty and published by American Mathematical Soc.. This book was released on 1993 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Curves, Jacobians, and Abelian Varieties by : Ron Donagi
Download or read book Curves, Jacobians, and Abelian Varieties written by Ron Donagi and published by American Mathematical Soc.. This book was released on 1992 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on the Schottky Problem, held in June 1990 at the University of Massachusetts at Amherst. The conference explored various aspects of the Schottky problem of characterizing Jacobians of curves among all abelian varieties. Some of the articles study related themes, including the moduli of stable vector bundles on a curve. Prym varieties and intermediate Jacobians, and special Jacobians with exotic polarizations or product structures.
Book Synopsis Complex Abelian Varieties by : Herbert Lange
Download or read book Complex Abelian Varieties written by Herbert Lange and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Arithmetic of Elliptic Curves by : Joseph H. Silverman
Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
Book Synopsis Moduli of Curves and Abelian Varieties by : Carel Faber
Download or read book Moduli of Curves and Abelian Varieties written by Carel Faber and published by . This book was released on 1999-06-29 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Complex Tori and Abelian Varieties by : Olivier Debarre
Download or read book Complex Tori and Abelian Varieties written by Olivier Debarre and published by American Mathematical Soc.. This book was released on 2005 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Abelian l-Adic Representations and Elliptic Curves by : Jean-Pierre Serre
Download or read book Abelian l-Adic Representations and Elliptic Curves written by Jean-Pierre Serre and published by CRC Press. This book was released on 1997-11-15 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Book Synopsis Moduli of Curves and Abelian Varieties by : Carel Faber
Download or read book Moduli of Curves and Abelian Varieties written by Carel Faber and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dutch Intercity Seminar on Moduli, which dates back to the early eighties, was an initiative of G. van der Geer, F. Oort and C. Peters. Through the years it became a focal point of Dutch mathematics and it gained some fame, also outside Holland, as an active biweekly research seminar. The tradition continues up to today. The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Hain, E. Looijenga, and F. Oort, originates from the seminar held in 1995--96. Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles.
Book Synopsis The Structure of the Moduli of Curves and Abelian Varieties by : David Mumford
Download or read book The Structure of the Moduli of Curves and Abelian Varieties written by David Mumford and published by . This book was released on 1970 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rigid Geometry of Curves and Their Jacobians by : Werner Lütkebohmert
Download or read book Rigid Geometry of Curves and Their Jacobians written by Werner Lütkebohmert and published by Springer. This book was released on 2016-01-26 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Book Synopsis Q-curves and Abelian varieties of GL2 [GL tief 2] - type by : Jordi Quer
Download or read book Q-curves and Abelian varieties of GL2 [GL tief 2] - type written by Jordi Quer and published by . This book was released on 1998 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abelian Varieties written by S. Lang and published by Springer Science & Business Media. This book was released on 2012-09-07 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is with considerable pleasure that we have seen in recent years the simplifications expected by Weil realize themselves, and it has seemed timely to incorporate them into a new book. We treat exclusively abelian varieties, and have summarized in a first chapter all the general results on algebraic groups that are used in the sequel. We then deal with the Jacobian variety of a curve, the Albanese variety of an arbitrary variety, and its Picard variety, i.e., the theory of cycles of dimension 0 and co dimension 1. The numerical theory which gives the number of points of finite order on an abelian variety, and the properties of the trace of an endomorphism are simple formal consequences of the theory of the Picard variety and of numerical equivalence. The same thing holds for the Lefschetz fixed point formula for a curve, and hence for the Riemann hypothesis for curves. Roughly speaking, it can be said that the theory of the Albanese and Picard variety incorporates in purely algebraic terms the theory which in the classical case would be that of the first homology group.
Book Synopsis Moduli of Abelian Varieties by : Allan Adler
Download or read book Moduli of Abelian Varieties written by Allan Adler and published by Springer. This book was released on 2006-11-14 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book aimed at researchers and advanced graduate students in algebraic geometry, interested in learning about a promising direction of research in algebraic geometry. It begins with a generalization of parts of Mumford's theory of the equations defining abelian varieties and moduli spaces. It shows through striking examples how one can use these apparently intractable systems of equations to obtain satisfying insights into the geometry and arithmetic of these varieties. It also introduces the reader to some aspects of the research of the first author into representation theory and invariant theory and their applications to these geometrical questions.
Book Synopsis Abelian Varieties, Theta Functions and the Fourier Transform by : Alexander Polishchuk
Download or read book Abelian Varieties, Theta Functions and the Fourier Transform written by Alexander Polishchuk and published by Cambridge University Press. This book was released on 2003-04-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Book Synopsis Modular Forms and Fermat’s Last Theorem by : Gary Cornell
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 2013-12-01 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, 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 an indispensable resource.
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