By Kai-Wen Lan
By learning the degeneration of abelian types with PEL constructions, this booklet explains the compactifications of delicate essential versions of all PEL-type Shimura types, offering the logical origin for a number of interesting fresh advancements. The ebook is designed to be obtainable to graduate scholars who've an figuring out of schemes and abelian varieties.
PEL-type Shimura forms, that are traditional generalizations of modular curves, are necessary for learning the mathematics houses of automorphic types and automorphic representations, and so they have performed very important roles within the improvement of the Langlands application. As with modular curves, it truly is fascinating to have quintessential types of compactifications of PEL-type Shimura types that may be defined in adequate element close to the boundary. This booklet explains intimately the subsequent subject matters approximately PEL-type Shimura types and their compactifications:
- A development of gentle indispensable types of PEL-type Shimura kinds by means of defining and representing moduli difficulties of abelian schemes with PEL constructions
- An research of the degeneration of abelian kinds with PEL buildings into semiabelian schemes, over noetherian general entire adic base earrings
- A development of toroidal and minimum compactifications of soft indispensable types of PEL-type Shimura forms, with targeted descriptions in their constitution close to the boundary
Through those issues, the ebook generalizes the speculation of degenerations of polarized abelian kinds and the appliance 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).
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Arithmetic Compactifications of PEL-Type Shimura Varieties (London Mathematical Society Monographs) by Kai-Wen Lan