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＜電子ブック＞
Degeneration of Abelian Varieties / by Gerd Faltings, Ching-Li Chai
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 22)

版	1st ed. 1990.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1990
本文言語	英語
大きさ	XII, 318 p : online resource
冊子体	Degeneration of Abelian varieties / Gerd Faltings, Ching-Li Chai ; : gw,: us
著者標目	*Faltings, Gerd author Chai, Ching-Li author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Number theory FREE:Algebraic Geometry FREE:Number Theory
一般注記	I. Preliminaries -- II. Degeneration of Polarized Abelian Varieties -- III. Mumford’s Construction -- IV. Toroidal Compactification of Ag -- V. Modular Forms and the Minimal Compactification -- VI. Eichler Integrals in Several Variables -- VII. Hecke Operators and Frobenii -- Glossary of Notations -- An Analytic Construction of Degenerating Abelian Varieties over Complete Rings -- David Mumford 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-662-02632-8

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