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|All Authors / Contributors:||
|Description:||xxiii, 561 pages : illustrations ; 26 cm.|
|Contents:||Definition of moduli problems --
Representability of moduli problems --
Structures of semi-Abelian schemes --
Theory of degeneration for polarized Abelian schemes --
Degeneration data for additional structures --
Algebraic constructions of toroidal compactifications --
Algebraic construction of minimal compactifications --
Algebraic spaces and algebraic stacks --
Deformations and Artin's criterion.
|Series Title:||London Mathematical Society monographs, new ser., no. 36.|
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 compacrifications 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.
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