Degeneration of Abelian varieties
Author(s)
Bibliographic Information
Degeneration of Abelian varieties
（Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge,
Springer-Verlag, c1990
- : gw
- : us
Available at / 91 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:516.3/F1992070184218
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Note
Includes bibliographical references
Description and Table of Contents
Description
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.
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