Degeneration Of Abelian Varieties

Author : Gerd Faltings,Ching-Li Chai
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 40,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662026328

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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.

Author : Gerd Faltings,Ching-Li Chai
Publisher : Unknown
Page : 336 pages
File Size : 47,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662026333

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

Author : Kai-Wen Lan
Publisher : Princeton University Press
Page : 584 pages
File Size : 40,5 Mb
Release : 2013-03-21
Category : Mathematics
ISBN : 9781400846016

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Arithmetic Compactifications of PEL-Type Shimura Varieties by Kai-Wen Lan Pdf

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties. PEL-type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in the development of the Langlands program. As with modular curves, it is desirable to have integral models of compactifications of PEL-type Shimura varieties that can be described in sufficient detail near the boundary. This book explains in detail the following topics about PEL-type Shimura varieties and their compactifications: A construction of smooth integral models of PEL-type Shimura varieties by defining and representing moduli problems of abelian schemes with PEL structures An analysis of the degeneration of abelian varieties with PEL structures into semiabelian schemes, over noetherian normal complete adic base rings A construction of toroidal and minimal compactifications of smooth integral models of PEL-type Shimura varieties, with detailed descriptions of their structure near the boundary Through these topics, the book generalizes the theory of degenerations of polarized abelian varieties and the application of that theory to the construction of toroidal and minimal compactifications of Siegel moduli schemes over the integers (as developed by Mumford, Faltings, and Chai).

Author : Christina Birkenhake,Herbert Lange
Publisher : Springer Science & Business Media
Page : 638 pages
File Size : 45,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662063071

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Complex Abelian Varieties by Christina Birkenhake,Herbert Lange Pdf

This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. ". . . far more readable than most . . . it is also much more complete." Olivier Debarre in Mathematical Reviews, 1994.

Author : Gerard van der Geer,C. Faber,Frans Oort
Publisher : Birkhäuser
Page : 526 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883030

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Moduli of Abelian Varieties by Gerard van der Geer,C. Faber,Frans Oort Pdf

Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This 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.

Author : Carel Faber,Eduard Looijenga
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783322901729

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Moduli of Curves and Abelian Varieties by Carel Faber,Eduard Looijenga Pdf

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.

Author : Moshe Jarden,Tony Shaska
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 51,7 Mb
Release : 2021-05-03
Category : Education
ISBN : 9781470452070

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Abelian Varieties and Number Theory by Moshe Jarden,Tony Shaska Pdf

This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanoes, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfeld modular varieties, representations of etale fundamental groups and specialization of algebraic cycles, Deuring's theory of constant reductions, etc. The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.

Author : Valery Alexeev,Arnaud Beauville,Charles Herbert Clemens,Elham Izadi
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 45,5 Mb
Release : 2008
Category : Abelian varieties
ISBN : 9780821843345

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Curves and Abelian Varieties by Valery Alexeev,Arnaud Beauville,Charles Herbert Clemens,Elham Izadi Pdf

"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.

Author : Martin C. Olsson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 50,9 Mb
Release : 2008-08-25
Category : Mathematics
ISBN : 9783540705185

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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.

Author : Alexander Polishchuk
Publisher : Cambridge University Press
Page : 308 pages
File Size : 49,8 Mb
Release : 2003-04-21
Category : Mathematics
ISBN : 9780521808040

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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.

Author : Ke-Zheng Li,Frans Oort
Publisher : Springer
Page : 123 pages
File Size : 46,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540696667

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Moduli of Supersingular Abelian Varieties by Ke-Zheng Li,Frans Oort Pdf

Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to Äg.g/4Ü, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).

Author : Umberto Zannier
Publisher : Princeton University Press
Page : 175 pages
File Size : 48,5 Mb
Release : 2012-03-25
Category : Mathematics
ISBN : 9781400842711

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Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181) by Umberto Zannier Pdf

This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by Umberto Zannier at the Institute for Advanced Study in Princeton in May 2010. The book consists of four chapters and seven brief appendixes, the last six by David Masser. The first chapter considers multiplicative algebraic groups, presenting proofs of several developments, ranging from the origins to recent results, and discussing many applications and relations with other contexts. The second chapter considers an analogue in arithmetic and several applications of this. The third chapter introduces a new method for approaching some of these questions, and presents a detailed application of this (by Masser and the author) to a relative case of the Manin-Mumford issue. The fourth chapter focuses on the André-Oort conjecture (outlining work by Pila).

Author : Ron Donagi
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 49,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851432

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Curves, Jacobians, and Abelian Varieties by Ron Donagi Pdf

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.

Author : David Mumford
Publisher : Debolsillo
Page : 0 pages
File Size : 44,9 Mb
Release : 2008
Category : Abelian varieties
ISBN : 8185931860

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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.''

Author : José María Muñoz Porras,Iberoamerican Congress on Geometry,Sevín Recillas-Pishmish
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 43,6 Mb
Release : 2006
Category : Abelian groups
ISBN : 9780821838556

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The Geometry of Riemann Surfaces and Abelian Varieties by José María Muñoz Porras,Iberoamerican Congress on Geometry,Sevín Recillas-Pishmish Pdf

Most of the papers in this book deal with the theory of Riemann surfaces (moduli problems, automorphisms, etc.), abelian varieties, theta functions, and modular forms. Some of the papers contain surveys on the recent results in the topics of current interest to mathematicians, whereas others contain new research results.