Read e-book online Arithmetic Compactifications of PEL-Type Shimura Varieties PDF

By learning the degeneration of abelian types with PEL buildings, this booklet explains the compactifications of tender vital types of all PEL-type Shimura forms, delivering the logical origin for a number of fascinating contemporary advancements. The booklet is designed to be obtainable to graduate scholars who've an figuring out of schemes and abelian varieties.

PEL-type Shimura types, that are typical generalizations of modular curves, are priceless for learning the mathematics houses of automorphic varieties and automorphic representations, they usually have performed very important roles within the improvement of the Langlands application. As with modular curves, it truly is fascinating to have indispensable types of compactifications of PEL-type Shimura kinds that may be defined in adequate element close to the boundary. This e-book explains intimately the subsequent themes approximately PEL-type Shimura types and their compactifications:

• A development of tender crucial types of PEL-type Shimura forms via defining and representing moduli difficulties of abelian schemes with PEL constructions
• An research of the degeneration of abelian forms with PEL buildings into semiabelian schemes, over noetherian basic whole adic base earrings
• A development of toroidal and minimum compactifications of tender quintessential types of PEL-type Shimura types, with designated descriptions in their constitution close to the boundary

Through those issues, the e-book generalizes the idea of degenerations of polarized abelian kinds and the applying of that thought to the development of toroidal and minimum compactifications of Siegel moduli schemes over the integers (as built by way of Mumford, Faltings, and Chai).