Degeneration of Abelian Varieties

Degeneration of Abelian Varieties

by Gerd Faltings, Ching-Li Chai
     
 

ISBN-10: 0387520155

ISBN-13: 9780387520155

Pub. Date: 12/28/1990

Publisher: Springer-Verlag New York, LLC

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

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Overview

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.

Product Details

ISBN-13:
9780387520155
Publisher:
Springer-Verlag New York, LLC
Publication date:
12/28/1990
Series:
Ergebnisse der Mathematik und ihrer Grenzgebiete Series
Pages:
316
Product dimensions:
9.21(w) x 6.14(h) x 0.38(d)

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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