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Degeneration of Abelian Varieties By Gerd Faltings

Degeneration of Abelian Varieties by Gerd Faltings

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Summary

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.

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Degeneration of Abelian Varieties Summary

Degeneration of Abelian Varieties by Gerd Faltings

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.

Table of Contents

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.

Additional information

NLS9783642080883
9783642080883
364208088X
Degeneration of Abelian Varieties by Gerd Faltings
New
Paperback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
2010-12-15
318
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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