Degeneration Of Abelian Varieties
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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.
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.
Degeneration Of Abelian Varieties
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Author : Gerd Faltings
language : en
Publisher:
Release Date : 2014-01-15
Degeneration Of Abelian Varieties written by Gerd Faltings and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Classification Of Irregular Varieties
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Author : Edoardo Ballico
language : en
Publisher: Springer
Release Date : 2006-12-08
Classification Of Irregular Varieties written by Edoardo Ballico and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
M. Andreatta, E. Ballico, J. Wisniewski: Projective manifolds containing large linear subspaces; - F. Bardelli: Algebraic cohomology classes on some specialthreefolds; - Ch. Birkenhake, H. Lange: Norm-endomorphisms of abelian subvarieties; - C. Ciliberto, G.van der Geer: On the jacobian of ahyperplane section of a surface; - C. Ciliberto, H. Harris, M. Teixidor i Bigas: On the endomorphisms of Jac (W1d(C)) when p=1 and C has general moduli; - B. van Geemen: Projective models of Picard modular varieties; - J. Kollar, Y. Miyaoka, S. Mori: Rational curves on Fano varieties; - R. Salvati Manni: Modular forms of the fourth degree; A. Vistoli: Equivariant Grothendieck groups and equivariant Chow groups; - Trento examples; Open problems.
Arithmetic Compactifications Of Pel Type Shimura Varieties
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Author : Kai-Wen Lan
language : en
Publisher: Princeton University Press
Release Date : 2013-03-21
Arithmetic Compactifications Of Pel Type Shimura Varieties written by Kai-Wen Lan and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.
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).
Curves Jacobians And Abelian Varieties
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Author : Ron Donagi
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Curves Jacobians And Abelian Varieties written by Ron Donagi 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 1992 with Mathematics categories.
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.
Complex Abelian Varieties
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Author : Christina Birkenhake
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Complex Abelian Varieties written by Christina Birkenhake 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 2013-03-14 with Mathematics categories.
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.
Moduli Of Curves And Abelian Varieties
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Author : Carel Faber
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Moduli Of Curves And Abelian Varieties written by Carel 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 2012-12-06 with Technology & Engineering categories.
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.
Abelian Varieties And Number Theory
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Author : Moshe Jarden
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-05-03
Abelian Varieties And Number Theory written by Moshe Jarden 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 2021-05-03 with Education categories.
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.
Moduli Of Abelian Varieties
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Author : Gerard van der Geer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Moduli Of Abelian Varieties written by Gerard van der Geer 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.
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.
Curves And Abelian Varieties
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Author : Valery Alexeev
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Curves And Abelian Varieties written by Valery Alexeev 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 2008 with Mathematics categories.
"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.