Arithmetic compactifications of PEL-type Shimura varieties / Kai-Wen Lan.

Format:

Book

Author/Creator:

Lan, Kai-Wen.

Series:

London Mathematical Society monographs ; new ser., no. 36.

London Mathematical Society monographs ; Vol. 36

Language:

English

Subjects (All):

Shimura varieties.

Arithmetical algebraic geometry.

Physical Description:

1 online resource (588 p.)

Edition:

Course Book

Place of Publication:

Princeton, NJ : Princeton University Press, 2013.

Language Note:

English

System Details:

Mode of access: World Wide Web.

Summary:

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties. PEL-type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in the development of the Langlands program. As with modular curves, it is desirable to have integral models of compactifications of PEL-type Shimura varieties that can be described in sufficient detail near the boundary. This book explains in detail the following topics about PEL-type Shimura varieties and their compactifications: A construction of smooth integral models of PEL-type Shimura varieties by defining and representing moduli problems of abelian schemes with PEL structures An analysis of the degeneration of abelian varieties with PEL structures into semiabelian schemes, over noetherian normal complete adic base rings A construction of toroidal and minimal compactifications of smooth integral models of PEL-type Shimura varieties, with detailed descriptions of their structure near the boundary Through these topics, the book generalizes the theory of degenerations of polarized abelian varieties and the application of that theory to the construction of toroidal and minimal compactifications of Siegel moduli schemes over the integers (as developed by Mumford, Faltings, and Chai).

Contents:

Frontmatter

Contents

Acknowledgments

Introduction

Chapter One. Definition of Moduli Problems

Chapter Two. Representability of Moduli Problems

Chapter Three. Structures of Semi-Abelian Schemes

Chapter Four. Theory of Degeneration for Polarized Abelian Schemes

Chapter Five. Degeneration Data for Additional Structures

Chapter Six. Algebraic Constructions of Toroidal Compactifications

Chapter Seven. Algebraic Constructions of Minimal Compactifications

Appendix A. Algebraic Spaces and Algebraic Stacks

Appendix B. Deformations and Artin's Criterion

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9781299333000

1299333001

9781400846016

1400846013

OCLC:

832314069