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Degeneration of Abelian Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 22) - Hardcover
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.
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- PublisherSpringer
- Publication date1991
- ISBN 10 3540520155
- ISBN 13 9783540520153
- BindingHardcover
- Number of pages330
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DEGENERATION OF ABELIAN VARIETIE
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Degeneration of Abelian Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (22)) by Faltings, Gerd, Chai, Ching-Li [Hardcover ]
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Degeneration of Abelian Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 22)
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Degeneration of Abelian Varieties
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Degeneration of Abelian Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 22)
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Degeneration of Abelian Varieties
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Springer Berlin Heidelberg Jan 1991
(1991)
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Book Description Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 336 pp. Englisch. Seller Inventory # 9783540520153
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Degeneration of Abelian Varieties
Published by
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ISBN 13: 9783540520153
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Book Description Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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. Seller Inventory # 4892218
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Degeneration of Abelian Varieties
Published by
Springer Berlin Heidelberg
(1991)
ISBN 10: 3540520155
ISBN 13: 9783540520153
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Hardcover
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Book Description Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783540520153
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Degeneration of Abelian Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 22)
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(1991)
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Degeneration of Abelian Varieties (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a Series of Modern Surveys in Mathemati)
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Book Description Hardcover. Condition: Brand New. 1990 edition. 318 pages. 9.20x6.30x1.00 inches. This item is printed on demand. Seller Inventory # zk3540520155
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